The difference is that Peter Pan is a much-loved film that contains only a few problematic scenes. One’s main association with the movie isn’t the historical treatment of Native Americans (leaving aside the fact that the Indians of Neverland are fantastical anyway). Song of the South, by contrast, is much more difficult to disentangle from the historical and ideological issues that render it problematic in many people’s eyes, which is why Disney has essentially disowned the film these past thirty years (at least in the US).
Original MK harkens back to time when children engaged in playacting. The lands of MK pretty closely fit with the popular playacting games children often played. Sometimes they pretended to be astronauts, or jungle explorers, or pirates.
Back then, children were simply told to go play outside most of the time, and were otherwise mostly left to their own devices. If you were over the age of like ten, and had some minimal campfire-safety training, you were even allowed to light off firecrackers and bottle rockets. Boys had jackknives and cap guns. You just weren't supposed to actually stab each other with them.
I think most people nowadays have no clue, because most children don't playact. They don't roam as the once did, and they have more access to much better virtual games, and FAR more plastic toys than children did in the past.
Generally, the game of playing astronaut was you pretended your play area was outer space. Kids would pretend the floor was lava. So the game was that you'd try to walk/climb around your play area without ever touching the ground. We literally had a red carpet in our house, so it was easy to imagine the floor was lava. Much of the game revolved around debating which objects would 'melt' and which ones wouldn't and how long you could use each object before it melted. Couches didn't melt, but pillow sank quickly into the imaginary lava, usually faster than anyone could step on them! It also often ended in a debate whether women would ever be allowed in space.
Another game was to play 'princess,' Princess was mostly for girls. It involved getting into your mother's costume jewelry, make-up and dresses. It often ended when you realized your mom was going to kill you for spilling nail polish or breaking one of her lipsticks. Though boys also liked to pretend to be knights.
Another game was to pretend you were the characters of Tom Sawyer, but mostly just Tom and Huck. Much of the game involved setting up your fort. During recess, you maybe spent time deciding which part of the playground was what. Even better, you made your own fort out of blankets indoors or, if you were lucky, you made a real fort in the woods! Making a lean-to fort in the woods was the best!
Cowboys and Indians was another game. (I don't think the term "Native Americans" existed back then, or maybe it just wasn't well-known.) Pretending to be a Native American meant you wanted to be free, as in you wanted to be liberated from your parents and teachers. Both roles were generally respectable, but the cowboys were slightly less respected. Firing a gun was fun, but prowess with a bow was more respected. If nobody wanted to be the cowboy, then you could also pretend to be same/different tribes. Again, this could be played on a playground, but playing in the woods was best. This game was sometimes started when someone found a big feather, because a nice feather = a headdress. Often though, the game involved some kind of battle between the two sides.
In 2020, I'd say the depictions in the Peter Pan ride are an overt concern. When children pretended to be Native Americans they actually tried to be 'authentic.' Of course kids were far too naïve and uninformed to be authentic though, so the pretend version of Native American's is clearly based on stereotypes of real people.
Mind, I'm old enough to remember when Frontierland sold fake fur racoon hats and cap guns that actually looked like guns and rifles, and get this - the guns didn't even have bright orange plastic on the end.
It was a very different time. In some ways, today is much better. On the other hand, it feels like people have forgotten how to use their imagination.
That said, I'm uncomfortable with the idea of ranking anyone's unhappiness, discomfort, or pain against someone else's.