Agree but...I think this comes from parents and the wider family in those cases!
I've seen that for sure. But I think the categorisation thing also comes from pop culture. My teen daughter didn't go to school until she was about 12 so was fairly isolated from the worst of that, but when she did I was shocked at how powerfully that message came from the schools. Not even so much from the other kids at first, it was all rallies about this or that, the Rainbow club, signs about how many genders there are on the walls, several novels about trans kids appearing in the library (the one without enough books for research projects.)
My sense of where many parents miss out is in the rootedness of the person. I think maybe you have to teach that or at least talk about it in a more specific way than people often realise, and it isn't just about being affirming. Kids need to know, what makes a person valuable, have dignity, what is human life for or about. Not that they will always agree with parents, but it's a starting place. They need language to talk and think about things too. That isn't happening, at my university most students are coming into undergraduate degrees with no language to talk about ideas like that, and often no concepts around them either. All they have is the identity language.