For about five minutes in human history, we actually reached a situation where if women said "NO" to men, they were listened to. Then men found a whole new way to say, but we are the masters and we say "YES".
There is something both surreal and appallingly predictable about a bunch of men discussing which other men they will decide women have to tolerate in their single-sex spaces. It seems it was ever thus.
You know what? No genital inspections. None. I do not want to know what a man has in his pants, and if I ever find out, the situation has gone a long way in a direction I do not want it to go in at all. We can tell the difference between men and women perfectly well, with clothes on. The really, really easy way is, no men in women's spaces. None at all. Then we don't have to do any of that genital inspection thing, or even "papers please" (which would be forged anyway).
An assumption that men discussing this issue always make is that men will try to get in anyway, even if they're not legally allowed in. Funny thing though. Until about last Tuesday they generally didn't. Yes there were the so-called "true trans" LARPers trying it on, but there weren't many of these, and the point is that if they put so much as one size-13 foot wrong, they were in the wrong and the concerned women could challenge them and call for the attendant. Or even the cops. Lets try going back to that. It worked quite well. As opposed to the current situation where a man can do pretty much what he likes, and it's the woman who challenges him who gets called a transphobe and charged with a hate crime.
You are all making a bit too much of the danger of rape or sexual assault. Yes it happens and there are lists of "transwomen" who have attacked their victims in the women's toilets if you want them. Voyeurism is another issue of course. But the widespread, universal concerns are propriety, modesty and decency. These are particularly acute for women who have been the victims of severe sexual assault and women of certain religious groups, but they are issues for the majority of women. We don't want men in our intimate spaces because they're men, not primarily because we think they'll rape us.
As someone said on Twitter yesterday, "My husband and my two grown-up sons are absolutely lovely men who would never hurt any woman. I vouch for them. They should be allowed in women's single-sex spaces." Well we all know it doesn't work like that. Consent isn't transferable, and one women's belief that a certain man is "safe" doesn't need to be accepted by another woman on trust. And any man, no matter how nice, is a violation of what should be a women-only space.
Men with identity issues should not be women's problem to solve. Women's spaces are not therapy rooms for mentally ill men. Find another solution. We have got to the stage where if a certain class of men see any space at all that has "Women only" at the entrance, all he can think about is getting in there. Toilets, changing rooms, social media apps, rape crisis centres, a small boutique gym, the girls' swimming team. Doesn't matter how much provision there is that is open to men, including trans-identifying men, they want in the women's space. And if threats of violence don't work, he'll go to law. Maybe ask why. (The gym thing was just ridiculous. A woman set up a small gym in London just for women, and was immediately piled on by TRAs from all over the world insisting that this was transphobic and she MUST include men as well, and issuing all sorts of threats. There are plenty mixed gyms around, but their point is that there must not be any facility where they aren't allowed. Apparently it's fine to have trans-only facilities though.)
The very LAST men who should be allowed in women's single-sex facilities are the ones who want to be there. That should be fairly obvious.
It's probably true that some men will try to gain entry anyway. But they hardly ever pass, not in the flesh, a few feet away, and that goes double if they open their mouths. If the very occasional convincing ladyboy gets away with it because nobody notices, well, it's not ideal but that's life. Perfection is seldom attainable. What we need is to go back to the situation where these spaces were genuinely single-sex, and any man who thought he would go in anyway is putting himself in the position that someone may object to his presence, and she will be in the right.