SorryPleaseTryAgain (very appropriate name! I'll try...)
I wrote
"Something which occurs to me sometimes is that a lot is always said about women who because of their strict faith (I assume Muslin, Orthodox Jewish, some sects of Christianity?) cannot/absolutely may not use facilities or be in spaces in which they may have to encounter a partly-clothed male-bodied person, or indeed be close to an unrelated-to-them male-bodied person at all if there is nobody else present.
"Isn't the same true for observant male members of the same religious beliefs, but reversed: they absolutely must not be alone or in close proximity with a female-bodied person who is not directly related to them? I'm thinking here of Orthodox Jewish men asking to have a female person moved from the seat next to them on an aeroplane, or of Mike Pence never being alone with a woman, and I'm sure there are plenty of other examples. Third space facilities would be of no use to them, so they need male-body-only spaces in the same way that religious women need female-body-only ones. Having only third space facilities definitely isn't the answer for them any more than mixed-sex ones is."
I understand the OP as meaning keeping the two single sex spaces (male only, female only) and adding a third mixed sex space which anyone can choose to use if they don't want to use the single sex space for their sex (not gender/gender identity).
So surely the orthodox jewish men could then use the male only space?
Yes, they could, can and do, provided it really is a male only space. In the same way, strict-religious women can use the female only space provided it really is a female only space.
Neither group would not be able to use a mixed-sex space. I was agreeing with the OP.
But is far as I can make out only the women are ever used as an example of why having only mixed-sex spaces is the wrong way to go; never the men. Or at least, I don't recall such men ever being mentioned in this context; but surely they have a problem with only third spaces too?
(And that makes it another strike against the law, because religion, like sex, is a protected characteristic.)