Huh. ETA, sorry for the crazed bold and random asterisks. I may feel strongly, but that wasn't my intention! Hopefully it's all gone now...?
You keep coming back to your own perception of these women's interiority as the deciding factor, Crafty. Can you see that some readers here may see that as denying them meaningful autonomy? You're making the decision for them. You may be trying to do so sensitively and empathetically by reading the room as carefully as possible... but you can't avoid that fact that all you have to work with is their external signifiers of support, and your interpretation of these. The moment you join the club, their actual subjective reality becomes secondary to your own. You can never know their true views on the situation for certain.
And, yes, that's a sad fact of human experience (and one I struggle with, always trying to guess others' thoughts and emotions!) But it's precisely because it's a sad fact of human experience that society functions by respecting the various ways in which others delineate their boundaries. This would include permitting females the use of the word "woman" to be able to distinguish themselves, and respecting its application.
It's worth mentioning that it's transactivism, and the utter intransigence of posters like P, that have led me to take this harder line. TRAs have taught me that, to such as P, gracefully conceding your own (potentially, yes, entirely welcome) attendance at the book club is seen as synonymous with offering up the word "woman" itself on a silver platter. And that, women can't afford to do.