The muddle with sex and gender would seem to be at the bottom of it, resulting in the Trojan horse tactic of trying to sell you one (sex) when it's actually the other (gender).

Poor understanding of the relevant science as well as of the "probabilistic" nature of biological definitions is probably a factor. It's just so much easier to go by the immediately apparent surface phenomena — "if it looks and acts like a woman (whatever that means), it is a woman". Within discourses heavy on the autonomy of the individual it's easy to go along with pure subjectivism as well, "if you feel like it, you are it".

I think there's some research on people's poor intuitive understanding of likelihoods like "80% certainty". I think this was on some relatively recent episode of Sean Carroll's Mindscape podcast, but I cannot remember which episode (sorry!!). But if something had an 80% certainly attached to it and it doesn't happen after all, people will tell you, "but you said it's going to happen", because they took "80% certainty" to mean "almost guaranteed".

Intuitively people seem to understand 0% and 100% likelihoods, as well as fifty-fifty, the latter meaning, "it might happen or it might not". But that's it. It wouldn't be surprising if this kind of intuition would apply to category definitions as well.

So if you've got the kind of definitions as you do in biology, where there's always corner cases (like easily result from atypical development in complex systems), then that kind of definitions would appear to be invalid, because either something is X, or it isn't. If not all women have XX, then the XX definition of a woman must be invalid, even if it applies to 99% of the cases. Definition falsified!

This is to take a charitable view on the confusion. No doubt some people are fanning the confusion because it works for them.