Look, either "gender identity" is linked to physical sex, or it isn't and it's a free-floating feeling. They can't have it both ways.
Is there something -anything - physically female about a 'woman', or not? If everyone who is defined as a woman (NB - that would require a definition, which has never been forthcoming, ever) has a common factor, then we could confidently say who is and who isn't a woman.
If there is no such thing as 'a woman' that can be defined, then it's a meaningless word and having a gender identity (man, woman, non-binary, whatever) is meaningless, tells us nothing.
At some point, you have to name even one. single. criterion. for being a woman or a man. Or accept that each word just means 'an adult human' and go about life using that definition with no distinction between man, woman, non-binary, etc.
I don't really get why the conversation gets so bogged down with 'intersex' 'hormones' 'experience' 'toilets' 'cis' 'aligning' 'sexuality'. Either, when you use the word 'woman', you know what you mean and can explain that, or you don't. Start from there.
Basically what the OP is asking, in a roundabout way.