This is such an interesting thread - so many thought-provoking posts. I'm really grateful to everyone who's taken part.
I was mulling it over all the way home on the train. Two posts in particular, along with Kim's posts, have really made me think; and I'd like to be very clear, before I say anything else, that I'm not claiming to be expanding on what the posters in question were saying or extrapolating from what they said. I don't want to put words in anyone's mouth, I'm just trying to articulate my own (pretty inchoate) views.
This is an absurdly long post. The tldr, basically, is "I think women living under patriarchy communicate with other women in a unique way which is necessarily inaccesible to males, and therefore I wonder about the authenticity of the version of femaleness that transwomen base their female identity on."
In response to kim asking how Apocalypse knew that her sonographer was born female, Apocalypse said (among other very interesting points) there's a way women who are raised women communicate at these times, so even if she hadn't the same experience, the socialized woman to woman atmosphere would have been there.
This is REALLY interesting to me - so obvious now that it's been pointed out but I just never really thought about it before. I have never had a miscarriage, but I have female friends, family and acquaintances who have suffered miscarriages, and they've all spoken about the experience to me and in front of me in situations when no males were present. So even though I've never suffered this very unique loss, I know how women speak to each other about it. I've also been present when they've spoken about miscarriage in the presence of males, and the conversation is different.
This made me think about how women talk to each other and relate to each other when no males are present; and I think it is a "thing," if you know what I mean. I have very good male friends and very good female friends, and we all love each other and get on very well, and the conversation is in no way stilted when we are in mixed-sex groups. However, the conversation is different, to me, when there are no males present. Not just the topics we talk about, but also the way we talk and the way we listen, if that makes sense? It isn't worse, but it is definitely different. And, crucially, I have never seen my experience of females relating to females in private depicted accurately anywhere. CBG talks about this so eloquently here (google "culturallyboundgender i'm not like those other girls" if you're link-wary).
Basically what she says is that mainstream media's depictions of female relationships are almost always written by men (or edited by men, or in some way influenced by men's ideas of what female relationships looks like) and they are therefore inaccurate and inauthentic, and don't really ring true to actual women. I agree with her. The only TV show I can think of off the top of my head which features woman-to-woman conversations that seem really realistic to me is Roseanne, particularly when Roseanne is talking to her sister. Obviously, Roseanne was massive in its day so there were huge numbers of writers involved, but Roseanne Barr was very heavily involved in the writing and I think it shows.
What I'm trying to say is that, in my own experience, with my own friendship groups, over the course of my life, the presence of males subtly but significantly alters the way the women relate to each other. This means that the way females relate to each other is invisible to males (observer effect): we don't do it when they're around, and it isn't accurately replicated in movies or TV shows.
The reason I am wittering on about this is because kim asked, repeatedly, how we would know if a woman we were dealing with had a penis (or had had a penis) if they looked very feminine when we met them. To me this sounds like from kim's point of view (and I am NOT saying this an an accusation, but only as my attempt to understand what you are saying, kim - I know that you'll tell me if I'm wrong) the only, or at least the most important, defining characteristic of being a woman is looking like a woman.
And obviously I don't think that a particular appearance is the essence of being female. But it has also made me think about how transwomen think born women relate to each other. Transwomen are obviously at a disadvantage here, because having been born male and socialised as male, they have never really been exposed to female-only spaces, so where do they get their ideas about how females relate to each other? From TV? From movies? From adverts? None of those is an accurate representation in my opinion: none of them depicts the most common scenes from my own best friendship, which involve lying on sofas and either watching gemstv and shouting with outrage at how ugly the jewellery is and how hilarious the prices are, literally for hours on end, or putting Bad Boys on for the 40th time and then making the same comments at the same points. Anyway... I do wonder how the "hidden-ness" of women's relationships impacts on a transwoman's ability to pass.
It's also made me look again at the very strong push among vocal transactivists to shut down conversations about menarche, menstruation, pregnancy, female contraceptives, abortion, menopause etc. Previously I thought that the reason transwomen disliked these conversations was because transwomen had never and wold never experienced menarche, menstruation, pregnancy, female contraceptives, abortion and menopause.
Now I wonder if it's because transwomen's version of womanhood was formed with absolutely no exposure to these conversations, which typically happen only between women, and are NOT replicated in TV or film representations of women's conversations. So not only have transwomen never had any of those experiences themselves, but they have also never had exposure to women's conversations about them, and that is really threatening. I have never had a baby (I've been pregnant twice and had two abortions) but I have been privy to countless conversations about pregnancy and childbirth by virtue of being a woman myself; and I've never felt the need to shut down a conversation about pregnancy or childbirth that was happening in my presence, probably because I have been exposed to them since I was quite young and I am consequently fluent in the language now.
The other comment that really made me think was CaptChaos's mention of a transwoman lamenting having been robbed of a girlhood most of us wouldn't recognise, full of dolly's teaparties and frills and flounces. I spent my own girlhood dragging around a "doll" (if you could even call it that) which was fucking HIDEOUS, in every way imaginable: it was bigger than me, for a start; it had a rigid moulded plastic face and a fabric body tightly stuffed with wadding; the top of its head was made of fabric shaped like a dunce's cap and stuffed with wadding so it pointed straight up. I was obsessed with it and took it everywhere so it was filthy - absolutely rancid. No fucking way could you have taken that thing to a tea party. My sister and I loved making fires and snuck away craftily with our mother's matches whenever we could, and went and crouched behind the trees at the back of the garden, furiously trying to set dry leaves alight. I spent hours with my best friend gathering "poisonous" berries in her garden to make a potion to kill our mortal enemy. We also spent a LOT of time in her swimming pool, which was perfectly circular, running round and round right up against the wall, trying to create a really powerful vortex into which we could lure her sister 
Which is all to say, I do not recognise or identify with the girlhood or the womanhood that the most vocal transwomen describe, either in terms of how they are supposedly experienced firsthand or in terms of what the relationships between girls and women are supposed to look like. It really concerns me that my own life is not good enough (?) to qualify as "woman" because it doesn't look like man-made versions of girlhood and womanhood.