Quite.
They don't have passes. There's no one on the door. If 'Paula' wants in and any other man can come in then he's coming in. As with several cases, these individuals also tend to be repeat offenders. In one case I'm thinking of, the chap leaves prison, knocks up his new offenses and trots back inside again for another year or so, there's a trail of victims behind him.
There is no way to differentiate between a man who is genuine, a man who is not, many of the men who end up in court in such cases were genuinely living a transitioned life. The population contains dodgy members, as does any population.
Having committed serious sex offenses in women's spaces is no barrier at all to a GRC. And no one's checking anyway. It's not like a man gets his magic pass or wigs removed once he offends, he's as free to live as he pleases like everyone else.
Third spaces that women access by consent are the only possible answer that don't involve just shrugging and leaving the collateral damage of women to be an ugly but worthwhile side effect.