In regards to some previous comments about branding and what to do with some of the things Fox owns, I would like to add some comments. I think Fox has a greater association with epic action movies, general action movies, crasser movies and tv shows, more dramatic movies, more controversial movies and tv shows, and more dramatic movies than movies that come out under the Disney brand. However, they have also made family oriented movies like Disney has.
Fox apparently owns many of the movies and some of the tv shows produced by New World Pictures. Many of these have similarities to some of the movies made by Miramax after Disney purchased them in that they are what many people would describe as 'schlocky' movies. These have some similarity to some of the Tarantino movies made with Miramax and some movies by Robert Rodriguez who made some movies with Miramax. Many of the movies made by New World Pictures were made by Roger Corman. Interestingly, New World Pictures has a history with the Marvel company.
I think Fox could have some branding association with it at least when compared to some of Disney's channels due to it's name and names of some of the channels it owns. I am thinking that part of what the FX and FXX channel names could connote to English speaking viewers is that the content of the channels might be usually or always more 'extreme','explicit', and/or less child-appropriate than the content on some or all other Disney owned channels. The X in English speaking societies also seems to have an association with alcohol and erotic materials like strip clubs and ography. I think Disney would generally not want to bring up associations with the latter much, but the name FXX seems to already bring it up somewhat, but I don't think they try to lean much towards an association with erotic or ographic material but rather lean more towards an association with crass and extreme programming. I think the FXX name was chosen while these connotations were known by the people relevant to the choice of the name and that they still went with the choice for the name with this knowledge. I don't think they simply added an X to FX without knowing these connotation among some people.
This connotation and association with the X in the name and the idea of 'extreme' and 'explicit' might seem kind of cliched, but as long as there isn't a ad campaign bringing up that FX is 'extreme' that many people find foolish and silly, I think many people wouldn't find the idea silly or cliched. Many people might not really think about the X and it's association with programs that are less appropriate for children and may just notice that the programs on the FX and FXX channel would tend to or always be less appropriate for children than the programs on other channels owned by Disney.
Additionally, these connotations with the letter X in English speaking societies could also extend to theatrical films. If Disney were to release films with the name of FOX or 20th Century FOX or some other similar names which I'll discuss later, they could also have some people create an association with past 20th Century Fox movies that tend to be more extreme or different in some ways from many movies in the past that Disney has released with the Disney name. I've mentioned some of these differences in tendencies between 20th Century Fox movies and movies released with the Disney name on them above.
Something else interesting is that this X could even extend to the X-Men or at least the X-Men in theatrical films rather than in tv shows and past cartoons. However, this X could also extend to X-Men tv shows as well if desired. The X could extend to the past and potentially future X-Men movies by these movies in the past and in the future tending to be 'darker' in tone, 'darker' in cinematography, and possibly generally having fewer jokes than MCU movies outside of some X-Men movie series such as Deadpool and/or movies focused on the group or members of the group called 'X-Force'. Even for Deadpool, the X in FOX can still have relevant connotations in how the much of the movie is generally believed by many to be more 'extreme' in terms of violence, language, and maybe some other things than MCU movies and some other superhero movies.
Partly due to this, I think if Disney purchased FOX, Marvel should at least not immediately try to incorporate the X-Men into existing in the same movie universe as the current MCU. The idea of the X-Men and other superheroes existing in the same movie universe seems kind of strange. I have seen many people wonder why mutants would be often reviled and discriminated against even including the X-Men while some superheroes that exist in the same 'universe' in the comics are not reviled nor discriminated against by many people. If this same situation were to occur in the MCU, there would somehow need to be some sort of explanation for this I think or it will detract from the movies to a significant degree for some people. Mutants could be in the MCU somehow if there was to be some way that superheros started to be hated and mutants started to arise in the population and they were disliked as well, but I think this might take away from the tone of the MCU that many people have become used to. Additionally, adding the X-Men to the MCU generally would likely require the MCU to change the focus of at least some of their movies to be about things people aren't used to them mentioning much in the movies such as discrimination. Adding mutants to the MCU also may generally just make the MCU more complicated to make movies about depending more specifically on how it was done and what other superheroes would be also in the MCU. Having mutants and non-mutant superheroes may also add many characters that may again make it more difficult to make movies. It may be simpler to just keep the X-Men in a separate movie universe that is maybe more dystopic at least in regards to how people in the movie universe perceive those with superpowers than the MCU movies generally are. I think this could also play in to the X in the name of FOX and even X-Men if desired. Some people may associate the X as possibly connoting a darker or more serious tone than the MCU movies. Maybe Disney and Marvel wouldn't like that however. Even if they wanted to have the movies to be more similar to the MCU in terms of style and tone, the X with the name of the movies could still create an idea among people that these movies aren't in the same movie universe as the regular MCU if it were branded as being the 'XMCU' or 'XMMCU'. This would again allow the X connotations to come into play in how things associated with FOX are somewhat separated and different from things more closely associated with Disney.
I imagine it has likely already occurred to Disney the possibilities of the connotations with the letter X and associations with the company FOX and other things. Like I said it seems like FOX realized this with calling a channel FXX and even had a show called The X-Files. There is also the association with FX and special effects for videos. That could go along with the work that James Cameron has done with ambitious attempts of the use of special effects in movies that are affiliated with FOX, but I'm not sure how much FOX tries to promote such a connotation or if Disney in the future would want to try to connote some sort of connotation like that with part of the FOX or FX company or with the an association with the FOX company in general.
Also, immediately making movies with the same characters as past X-Men movies might make some fans of some of the characters upset and have some problems with new movies and additionally it decreases the value of those past movies and merchandise relating to them. It also possibly might create somewhat of a negative reflection on some of FOX's past work if it makes it seem like to some people that those movies FOX did weren't good enough in the eyes of Marvel Studios and/or Disney. It's a bit of a different situation, but Disney hasn't yet tried to remake the Star Wars prequels or say that they aren't canon. The same is true of Indiana Jones 4.
Something interesting about FXX and FOX tv shows from the past and the present is that they have some animated tv shows that vary from somewhat appropriate for children such as The Simpsons to animated tv shows such as Archer that are not appropriate for children and seem to be aimed towards adult and late teen audiences. This is something Disney doesn't really have. Imagine if talent writing or generally working on animation aimed at adults could move to working on live action tv shows or movies aimed at adults or vice versa from live action to animation. There could even be switches involved from animated tv shows or movies more appropriate for children to live action things appropriate for children or vice versa. Also, there could be switches from animation not appropriate for children to animation appropriate for children. However, switches like this I believe are not something that Pixar tends to like to do and the same may be for Disney theatrical animation, but it occurs with Fox animation. Imagine if Disney could eventually get to the point that they could own one or more studio that makes some animated shows and movies that are similar in genre to some past adult oriented dramatic Touchstone, Miramax, FOX Searchlight, and 20th Century FOX movies and successfully have them aimed at the same audience as those movies. There could be some benefits in some cases like with some of the 20th Century Fox style movies where there could be some savings in cost by having the movie/show animated rather than primarily live action and a few cases where having it animated allows for some interesting cheaper possibilities (think of things like from Futurama, Star Trek: The Animated Series, Life of Pi, and The Red Turtle in terms of the savings in cost for animation rather than live action).
I guess I should say that in this post in general when I say 'appropriate for children' I don't necessarily mean that what I'm referring to is only aimed at children as an audience, although that may sometimes be the case. An example of someone that would have been interesting if Disney could have had him working on things for FOX is Dan Harmon. In the past he has helped with at least a draft of Kung Fu Panda, helped with the writing of Dr. Strange by reportedly adding more comedy, and has made a fairly popular animated show called Rick & Morty that is popular among people who are adults and in their late teens. Dan Harmon is kind of an outspoken guy however and has said some things that maybe Disney would prefer a person involved in tv shows and movies they would own would not say, but he is just one example. Wes Anderson is another example as he made movies with Touchstone and now is making a 2nd animated movie for Fox. The animated things that appeal more to late teens than many Disney animated things is something Disney doesn't have much of like Cartoon Network and Nick. It could allow for the possibility of adaptions or spin offs into or from live action movies or tv shows. It could even allow for things like animated action (maybe even something by Marvel) or dramatic animated tv shows or animated movies that were aimed at people in their late teens or in adulthood. The animated movie like that might not happen unless as something offered on a streaming network however.
Another topic is Fox Searchlight. Having Fox Searchlight and 20th Century Fox could be beneficial to Disney if Disney ever wanted to build one or more theme parks having to do with FOX or that feature many FOX movies. Fox Searchlight could function similar to Miramax and maybe Touchstone to some degree, except that there is an association with other FOX things such as FOX tv shows and 21st Century FOX movies. The FOX Searchlight and Miramax films have seemed to tend to make films that are trying to be more prestigious than many 20th Century FOX movies and movies released with the Disney name. So, Disney could possibly partly or totally use FOX Searchlight and maybe Touchstone to release movies that are trying to be more prestigious than many 20th Century FOX movies and movies released with the Disney name. Then talent behind some of these movies could transfer over and help with the creation of some 20th Century Fox movies. Disney would then benefit more from these talents than they seemed to do with talents from Miramax . Some movies from 20th Century FOX seem to tend to be somewhat more similar in style to many of the movies made by these talents at FOX Searchlight than movies released with the Disney name on them have tended to be. Talents from FOX Searchlight may then tend to find the idea of making movies for 20th Century Fox more appealing than they may have found making movies with the Disney name in the past. It seems like some of the talents from Touchstone and Miramax like Shymalan, Wes Anderson, Robert Rodriguez, Peter Jackson, and Tarantino didn't make many movies that are appropriate for children and could be featured in a theme park aiming to be mostly child-appropriate. Anderson, Jackson, and Rodriguez did make some, but if Disney were able to benefit from these child appropriate movies and movies that are less child appropriate then they could benefit more.
Additionally, another benefit of possibly purchasing FOX is the ability to make mini-series and movies that aren't appropriate for children while it being associated with a recognizable name other than Disney for a streaming service like Hulu. Talent from FOX Searchlight and Touchstone could even work on mini-series and movies for such a streaming service. Programs like these would help Disney's streaming service compete better with Netflix and Amazon who have similar style shows, mini-series, and movies.
There is a benefit of getting access to some of FOX's channels that I noticed. They could maybe do something different with Freeform and DisneyXD and FX so that there at least wouldn't be commercials on Freeform for horror tv shows that don't seem child-appropriate in-between parts of Disney and Pixar movies that are child-appropriate.
Further more, if Disney purchased FOX's share of Hulu, they presumably would be the majority holder of Hulu and therefore benefit from presumably having more control over the service. Also, they might benefit more from these connections with FOX Searchlight and Touchstone if they were to put these movies, mini-series, and movies that aren't appropriate for children on Hulu rather than making a new general service or on a streaming service that is referred to as a general Disney streaming service. Hulu is already established as a service in comparison to some new service Disney could make. Disney may wish to avoid some conflicts people may have with the idea of Disney putting things that aren't appropriate for children on a service that is mostly about Disney even if the things that are inappropriate for children can be blocked form viewing. This association with the connotations with the X in FOX in comparison to the Disney name again comes in to play here I think.
A minor thing in regards to branding I would want to note is that FOX's live action tv shows seem to tend to have similar cinematography in comparison to one another. I think CBS, NBC, and ABC also tend to do this with many shows on their channel as well. Maybe I am imagining things for some of these shows, but it is something I wanted to note. These cinematography similarities could even be extended to other things like mini-series or movies made for a streaming service or maybe even for some theatrical movies if desired to create a greater association between certain things. I'm not so sure if this would really be desired much for theatrical movies however except for maybe some spinoff movies and/or certain movie franchises.
Another idea I had in regards to Marvel and Fox was that Disney or Marvel Studios could have certain mini-series and tv shows or even movies based on some past Marvel comics be made by Fox or in co-productions with Fox that would be available on a streaming service with other tv shows, series, and movies associated with FOX rather than a streaming service just for the MCU or a catalog group of programs/movies of the MCU on a streaming service. This Marvel section of a streaming service associated with Fox and that is separate from most MCU movies/shows might be a good place to put the Marvel Netflix shows if Disney got the rights to them back. This would be good especially for the Marvel Netflix shows due to how they generally aren't appropriate for children. Additionally, past Marvel movies and some tv shows such as the Daredevil movie, Fantastic Four movies, Fox made X-Men movies, and maybe some or all X-Men live action tv shows could appear here. Maybe some movies based on Marvel characters, but not made by Fox such as the Spider-Man, Punisher, Ghost Rider, and some other movies could also appear in this catalog group for a streaming service if Disney could get the rights to them permanently or just to stream them there. Possibly, old X-Men animated tv-shows and movies and other Marvel animated tv-shows/movies that are child-appropriate would appear on a service with the MCU stuff rather than FOX as those animated things would probably be more in line with more of the target audience of the MCU movies than the X-Men movies. The animated shows and movies would just have a separate section on the MCU affiliated streaming service.
An idea I had was that FOX maybe in co-production with Marvel Studios could make other movies or shows that are based on Marvel comics that don't have to do with superheros such as Marvel's old romance, military, 'Western', and 'horror' comics. A recent example of something like this is the Riverdale tv show. Possibly some of these could be considered part of the MCU and fit the style, tone, and child-appropriateness of previous MCU movies, but I think many people paying for a group of MCU movies and shows wouldn't really want to pay for these shows/movies if they don't have to do with superheroes, so it may make more sense to include them on another streaming service or at least as part of a different catalog group. Additionally, if they didn't have anything to do with superheroes it might not be that appealing to say that they are part of the MCU unless they appear in a MCU show or movie that has to do with superheroes. That would probably only happen if they were a show/movie having to do with the military or a super powered 'horror' character like a werewolf or something. I'm not sure Marvel really wants to try to do something like that in the recent future at least.
Something else FOX could do is create a third movie/show universe separate from the current MCU and X-Men possibly in co-production with Marvel Studios. Some of the benefits of doing this is that it could make some things easier to write if you don't have to worry about the current or past MCU. You could also have the superheros be as powerful as the big MCU superheros and fight villains that are as powerful as the ones they often fight while having it make sense that you don't see the MCU Avengers and similar MCU superheroes. I'm not sure if Marvel would want to do this. However having the possibility to have it separate from Marvel somewhat by having it made by FOX or in co-production with FOX could allow some big MCU fans maybe to be more accepting of the fact that at least initially the universe wouldn't go along with the phrase sometimes associated with the MCU of "It's all connected." There could still be some crossover of the universes in the future however through a similar way it's occurred in the comics in the past .
Yet another thing interesting about having FOX would be to have streaming of certain things like certain e-sports events and maybe some media like some videos from Disney's network of YouTubers and videos from Vice Media (which Disney has a stake in) to appear on a streaming service associated with FOX rather than Disney. Vice Media in particular would go better on a streaming service associated with some programming from FXX.
Something they could do with Blue Sky due to its name is to release more unusual movies, maybe even ones that would be more similar to some movies called by many as 'arthouse'. For example, Fantastic Mr. Fox, Isle of Dogs, and the Peanuts movie to some degree fit kind of what I'm thinking. They are kind of different from much of Disney and Pixar's long theatrical movies although maybe similar to some short films made by them. I'm not sure about the financial viability of focusing a lot on movies like this. Also, I'm not sure if Disney would want the name Blue Sky to stay due to the usage of the phrase 'blue sky' in Disney imagineering. It has an interesting connotation that the movie makers might be more free to make something different from Disney and Pixar's usual style, but I don't know if Disney would want that association with the phrase 'blue sky' or to bring up the idea that Pixar and Disney animation talent aren't as free in their work as people at another company. I'm not sure what exactly is a part of 20th Century Fox Animation, but if there is a significant team with this name, they could maybe do something different from Blue Sky or be combined into them.