This post is probably going to be strongly disagreed with and lost in the barrage of posts on this issue, but I feel its worth sharing and explaining a few aspects regarding my opinions on this.
You should be able to look back on my post history and see that I was pretty strongly against most attraction rethemes: from Frozenstrom to Guardians. Out of the recent string of ride rethemes that Disney has done, I can genuinely say that this one bohers me the least by a pretty sizable margin. Enough to the point where I'm not just tolerating it, but supporting it. So... why? This seems like something that, based on my track record, I should be strongly opposed to. To make this a little easier, I'm going to compare it to another operating attraction at MK with some in poor taste cultural depictions and talk about how that could/should change and how that does and does not apply to Splash Mountain's case.
For the sake of this post, I will be comparing Splash Mountain with the Jungle Cruise. For starters, Jungle Cruise has a more clearly problematic portrayal of African people in the attraction, as seen in the head hunters section, where stereotypical "savage" images are used as a threat to comedic effect. Thankfully, this could easily be corrected by removing this one section and replacing it with another gimmick, maybe bring in the pirañas from DL or something. Regardless, it is one part of a larger attraction.
Splash Mountain is clearly different, in that its racist moments are not at all explicitly found in the attraction; in fact, the attraction even tries to hastily cover up some of the problematic moments ported over from the films. As one of many examples, Brer Rabbit's capture with the beehive honey is intended to replicate his capture with the "tar baby" (the name alone should throw up about five red flags). Or there is the way that Brer Rabbit is meant to evoke the mannerisms and actions of a slave (African-American Vernacular and all) while Brer Fox is effectively a white slave owner of the time. Finally, one of the most unknown offenders is the iconic song itself "Zip-A-Dee-Do-Dah" which is derived from blackface performances intended to actively mock the African-American population. The ties to racism is so intertwined with the attraction that it would be impossible to modify in the same way as Jungle Cruise. For JC you just get a new scene' for Splash Mountain, take away the way the Brers are presented, some of the tropes from the film, and the song, and you barely have a ride left. At that point, if you remove that, there has to be a conscious effort to keep Song of the South involved, which I can guarantee there is next to no desire to do.
As for "why Princess and the Frog?" it's really the only IP that could easily slip into both mountains. Sure it's a stretch in Frontierland, but so was Song of the South. As for the "yes, but why not keep Splash Mountain and give Tiana her own ride?" crowd: Splash Mountain was on borrowed time due to its irremovable ties to racist symbols, and (at least at DLR) there wasn't really a good spot to give Tiana her own ride. Really this kills two birds with one stone (and we don't have to see some god-awful visuals of Splash being demolished Horizons-style.
I know Splash is a sentimental favorite for many, but if we want a better future we need to account for past mistakes. Letting a ride that has inherent ties to racist portrayals of African-Americans would not let that happen.
As kind of a P.S., I've seen a lot of people suggest that Tony Baxter was forced into being involved with this. I have had it confirmed by different people that he wasn't, and that he was asked and he elected to be involved with this.