but gender traits are real and people have real (to them) identification with sets of gender traits that they call 'gender identity'. Not everyone does this so not everyone has a gender identity, but everyone has some or other gender traits, as it is part of being human.
Hmm. It's true that despite broad equality, men and women do behave in typical ways, and there is certainly male-typical and female-typical dress patterns. (Some of which arise in part from body shape, some is sexual signalling, some is pretty arbitrary).
And people have different levels of interest in how much they follow society-typical sexual signalling. Some conform by default, some take pleasure in conforming, some don't want to conform, some want to conform to the stereotypical opposite sex, and be treated as the opposite sex by sufficient opposite-sex signalling
But, and it's a big but, those who want to not conform, or want to conform to the opposite, are often seeming to follow rather odd stereotyped views.
Both transwomen (particularly heterosexual) and transmen often tend to dress in ways which really aren't very typical of the opposite sex in reality, but actually signal "too hard" in a rather stereotyped way. It's not really conventional "gender expression" of the opposite sex.
And that then distorts things, particularly for women. "Woman" as role-played by heterosexual transwomen is not something most actual women are going to relate to. Which seems to quite naturally be leading young women to decide that well, they're not "women" as per that characterisation, so they must be "non-binary".
But regardless of this "gender expression" - which may be excessively opposite-sex stereotypical, the actual behaviour patterns of transmen and transwomen remain very sex-typical. Transwomen are more violent, aggressive and overbearing, transmen are more self-concious. Behaviour remains very sex-typical, suggesting that this inner "gender identity" thing they claim to have - something in the brain - is not related to any sort of "innate biological sex role", nor does it show signs of matching the "gender identity" that the opposite sex is supposed to have.
I see no statistical common behaviour between transmen and men, and transwomen and women. No evidence of an "opposite-sex brain". Trans people generally behave like non-trans people of the same sex with the same sexual orientation.
So my rejection of it is not just really on philosophical grounds - I genuinely cannot see the behaviour difference you would expect to see if there was this "gender identity" commonality.