Same ideology supports both. I've also seen the kids that are a little too old for dress up and make up as animals out in public with their very progressive looking adults. And their actions didn't come across as play acting.
Coming out of the closet is an ideology. People that argued against slippery slopes, though a fallacy, inherently knew or at least highly suspected that the closets were a lot deeper than some thought and once mental illness was celebrated and supported, we were in for a ride.
You may see litter boxes as fallacies but once the restrooms are open and common to all, to think that "all" doesn't keep accumulating to accommodate all is simply naive. That was the discussion we were having during the marriage debates. Some of us said where we expected this to go. It went there and faster than we expected.