I see the appalling lesbophobia and it gives me the rage (and this is as a straight woman). How dare society expect women and more specifically lesbians to always make room, move over, 'be kind' and deny themselves what they need in order to give to someone else?
So many of the posters on this thread have completely missed the point that its not just a women's group, its a group specifically for lesbians, women who define themselves as same sex attracted, and therefore have different needs and wants to all women as a general group.
Can you imagine a room full of gay men accepting a wavering transwoman to join them because 'be kind'? No, neither can I.
While the trans man is, biologically, a woman, politically they are not - they have publicly rejected womanhood and want to use male pronouns. And this is a crucial and important distinction. In some circumstances this matters, and this is one of those circumstances (for those who would deliberately misunderstand this - I am not arguing that I think this makes them a male, it's not a gotcha 🙄).
Placed alongside the very odd circumstances of their sudden arrival, this it would make me very wary of their possible agenda, while at the same time feeling very sorry for them if they are thinking about detransistion and looking for friends & support. But if that's what they are looking for then its not your responsibility to provide it at the expense of your own safe space and in the current climate you are right to be very wary.
If you are still considering admitting them, it would be worth finding our their views on homosexuality and same sex attraction as it could be likely that they are significantly different to the views held by most of the group. As this the very reason the group exists, to support same sex attracted women, that difference could well lead to problems for the group if they join. They sound like a likely destabilising influence, and you are not obliged to accept that. Good luck with negotiating this hurdle and defending your space.