[flagged]
In the case of woman, the recognition is that "woman" as commonly used conflates two separate ideas: The gender that someone was assigned at birth (which in the vast majority of cases means someone's biology) and the social constructs that define "woman" (e.g. dress, role in society, acceptable behavior, etc.).
Separating conflated ideas allows people to think in more detail since they can consider them separately.
Don't confuse the meaning of the existing word and pretend it's necessary. That's another tactic is conflating categories. Usually there's some sympathetic category that is a tiny amount of people, like genuine at-birth hermaphrodites, and they argue about that while at the same time pretending all that stuff applies to men who want to be housed in women's prisons.
One thing that drives me nuts with this language stuff lately is how the word "Partner" came to mean romantic partner because people can't just be bothered to say "girlfriend" or "boyfriend" anymore. Now, when people introduce their "partner" in a context where it's ambiguous whether it's personal or business "partner" I have to wonder in which sense do they mean it.
You could use the power of the spoken word to ask them directly. You can ask probing questions if you’re not comfortable being that direct.
From far away (Europe) I don't see a big difference between the multiple "fanatical" groups that I hear about in US that define one thing or another "their way" and everybody else's opinion it's wrong. And that covers a wide range of topics (like: religion, guns, transportation, gender, etc.)
And just because some people are fanatical on a topic, does not mean there are not huge issues around those topics. Just as an example on gender, the horrible violence that was (and probably) inflicted to women (extreme examples: Pelicot and Fritzl cases)
But sure, it is easier to argue on useless definitions (either for or against) that try to address root causes...