This one is the one that makes me uncomfortable. I do not feel that men should be allowed access. But Trans-women? Gets sticky. I don't know.
Transwomen are men. If you let transwomen in, you are letting a subset of men in. That is not hate, it is biological reality.
However, it goes further than that. While human beings are excellent at telling men from women, telling men from transwomen is well-nigh impossible. The vast majority of transwomen have had no sex reassignment surgery, and even those who have still look like men unless you see them undressed.
If transwomen are legally allowed to be in women's intimate spaces, in practice that means that any man at all who wants to be there is allowed, because nobody can tell the difference and we're all rather against "papers please" at the entrance (and papers can be forged). As the speech I linked to above correctly states, "It follows that it is not possible to admit a biological male to a single-sex service for women without destroying its intrinsic nature as such: once there are XY chromosome adults using it, however they define themselves personally, it becomes mixed-sex."
Well-meaning commentators often feel they would like to admit the "nice" transwomen to women's spaces, while excluding the fakes and the chancers. It's not possible. Fakes and chancers look exactly like nice people, that's how they operate.
As I've said before, a number of times, it's the consequences of granting any subset of men the
legal right to be in women's spaces that are the problem. The granting of that right removes any possibility of policing these spaces to keep men out, including men who are there to perv or assault or generally creep women out. Challenge becomes impossible, because the man will simply claim a trans identity and accuse the challenger of transphobia and hate.
We did have a system where men were
not legally permitted in women's intimate spaces, but women were prepared to turn a blind eye to a poorly-passing transwoman who seemed to be doing his best to fit in and simply went in and out as unobtrusively as possible. That could continue. Yes, such a person could be challenged, but it's not very likely, and if challenged all that's needed is for the transwoman to apologise and leave.
However, the demands for legal rights to invade women's spaces irrespective of how uncomfortable it makes women have really screwed this up.