I don't know that freedom of thought is really relevant to the idea of identity. Identity in my view isn't constructed by the individual in the way that people seem to think. There is also a health angle to this - there is I think something very unhealthy about believing that you don't have to be self-critical about your view of yourself, that it can't be socially or personally damaging.
In any case, social identity, which seems to be what people mean when they talk about things like getting to pick their own pronouns, is absolutely not about a "right" that you have against other people.
The comment about computer gamers is on point I think, and I also believe it applies to what they seem to be calling "fandom" these days. I used to be active playing RPGs as a kid and teen, going to comic cons and such and of course we were weird kids in some ways. But I find some of the people at them now really odd, it's like they actually have tried to root their sense of identity in made-up characters and pop culture expressions. I notice the same thing with some of the things like drag or cross-dressing - it used to be that people seemed to understand themselves as separate from their roles, and now they don't always. You can be a "drag kid" because that is your essential self, somehow.
I also wonder if this sin't tied in a bit to some ideas we have about legal fictions. We seem to think the legal fiction of declaring you make yourself a woman, makes you one. But there are also examples that people have tended to accept. Adoption is a lovely thing, but there has been a push in some cases to want to say, the adopted parents are the "real" parents, not the biological ones. Even the marriage equality debate sometimes got into this question of, if the law declares a thing the same, it is the same, whether there are material differences or not.
It may be that we have been training ourselves, in a lot of areas, to think in those terms.