Honestly, that was one of my thoughts, too. I think the original question was intended to be rhetorical - correct answer: it would be wrong to be forced to out myself. But so many such groups are hosted in women's own homes. If I were hosting a stated women's book club, and a male attended, I could feel unsafe and would certainly feel misled. That the poster asking this felt the answer was self-explanatory suggests this hadn't occurred to them. In other words, transwomen and women are different. We each need the right to our own words and spaces!
What P is arguing to me seems to be, despite tens of pages so far, pretty simple. To permit "women" to have a word of their own that excludes males who self-identify as women is authoritarian overreach by a (necessarily sinister-sounding, with a capital "S") State that contravenes the norms of democratic society. Yes, transwomen and women can mix in a multitude of contexts. Yes, they can enjoy each others' company. But transwomen must be able to call themselves women. MUST.
When you get down to the bare bones of it, it's laughably absurd and deeply ironic. Fundamentally (another reoccurring word-family that's apt here on several levels), P wants to deny 51% of the population any word of their own. At all. And that 51% would be the half who only just got the vote less than 100 years ago, note (which seems relevant, given that democratic values are central to their convictions). And as such, by logical extension, P argues that a democratic society now should in fact deny this group the ability to distinguish and name themselves, and thereby to advocate for their needs and rights.
Meanwhile, other posters are repeatedly pointing out the infinity of ways in which transwomen and women may still enjoy each other's company, with the only limiting factor being that this isn't under the descriptor "Woman", as that word's long since been taken and remains urgently needed. They're patiently explaining the law, the ethics, the philosophy and the biology of this. Again, and again, and again. Only to face the same old rhetoric, with little nuance and no meaningful acknowledgement of their points.
I sure know which of the two viewpoints being presented in this thread sounds inflexible, sinister and even somewhat authoritarian to me...