They kind of already do/are. Disney- the big one, parent company of all the other operations, has a ton of divisions and independent operations. Most of them are in California. There was a plan to invest a billion dollars into an expansion into Florida last year that was canceled quite openly because of Florida politics. The only major piece of Disney that’s in Florida is Disney World, and its associated other offerings.
Now, if we were to consider the possibility of moving that, even ignoring the extraordinary cost to do so, we must first find a place to move it to. Geography is very important here- between Disney Land in California and Disney World in Florida, most Americans are within about a day’s drive. It’s also far enough south that it can operate year-round. This makes it a popular spot for us northerners to go to in the winter.
Georgia might be an option now, but it could only work outside of (but near) Atlanta. This is itself risky, since Georgia has and continues to push many of the same problematic right-wing and proto-fascist laws. But where else? You end up going pretty far north to Virginia before you get any semi-reliable assurances. Could a theme park work in a Virginia winter?
Texas might (very questionable) be safe due to their worship of corporations, but it goes very far west. That makes it a lot more difficult for those lucrative New Englanders, particularly New Yorkers. It also cuts into the audience for Disney Land.
Disney is a greedy corporation. They will operate Disney World however they can make the most profit. They might get creative- for instance, divesting the park and charging exorbitant licensing fees for whoever takes up the operations. This is similar to Hollywood accounting and how every movie loses money on paper. But if it comes down to it, they would stop any LGBTQ+ support if that ends up being more profitable.
You may have heard the stories that Walt himself was an anti-semite. He wasn’t, per se. He just had no problems running his business in a way that he could still sell movies to Nazi Germany.