I've been trying REALLY hard not to express my exasperation, particularly as others are explaining stuff so well. I have failed. This, to me, sums up the internal incoherence of the 'gender identity' fallacy:
Being non-binary isn’t about rejecting femininity or not fitting a mould, it’s about not identifying as solely male or female at all. So your example actually reinforces the point: gender identity is internal. You know you’re a woman.
You can't rationally agree that gender is a set of social constructs & stereotypes - which it is, as you have demonstrated, because it's situation dependent - and then segue into the assumption that gender equals sex.
Either a 'gender identity' is a self-evaluation in relation to the cultural expectations of each sex, or it's a statement that the person doesn't accept the sex of their body. It can't be both unless you're starting from the premise that gendered conventions determine sex.
Cultural mores do not determine sex. That much is obvious, I hope.
If you feel you don't want to be defined by your culture's rules on which sex can do what, then good for you. You're normal.
If you feel that the sex of your body dictates what you may or may not do, you're a victim of gender ideology or living in a deeply oppressive society. My sympathies either way, but it doesn't mean you have a special 'gender identity'. It means you're a fully functional human being who's being unfairly hemmed in by other people's beliefs.
If you feel you don't know, or can't accept, the fundamental fact of your physical sex, you've got a distressing mental health problem and I hope you manage to come to terms with it before too long. Because nothing can change your sex.
The PP you replied to knows her body's female. You seem to be saying this means she has a gender identity (female). Yet she's just said she's a female who chooses not to be hemmed in by 'gender'. So, by the parameters you've set out, she doesn't have a gender identity? But somehow she does?
It's incoherent. And, going back to your OP, YABU to think any gender identity is anything other than performative. It's an utterly depressing validation of society's gender rules. The more vehemently a person claims they must be trans/enby to exist outside those rules, the more power they yield to the rules.