It's just embarrassing to have to explain this again. Archie's presence, as of right, in a women's single-sex space, does indeed make it empirically less safe, even though he personally has absolutely no questionable motives at all and would not dream of harming another human being (other than, obviously, being entirely OK with making women uncomfortable because they're just bigots and deserve it).
We do not know which males are dangerous and which not. They do not come with "rapist" or "voyeur" or pederast" tatooed on their foreheads. It is not possible to tell based on what they are wearing. There's nothing, until they do something, and then it's too late.
If males are barred by law and custom from entering these spaces, experience has taught us one thing. The harmless, decent guys don't go in. If they do it's by accident and they rapidly reverse out with profuse apologies. So we know immediately who is potential trouble, and more importantly they have no right to be there. We can ask them to leave. We can call the management. We can beat a hasty retreat while we still can, and perhaps call the cops. This is as safe as we can reasonably achieve.
If however males are not barred by law and custom, this ability to police our space breaks down. First, we can't identify who should be regarded as potential trouble. We don't know this isn't Archie Gemmell Goal, all-round good guy, until he's made his move, and by then it will be too late. And second, we can't meaningfully police the space. If we're a bit suspicious we can't ask him to leave, or call the management. The best we can do is get the hell out as fast as we can. And forget calling the police, unless we want to be charged with a hate crime.
This space is no longer safe
This basically adds up to women self-excluding from their own spaces. Women watching to see if the coast is clear before they can go in for a pee. Women pairing up and agreeing to stand guard for each other while they go and fix their make-up. Nice sort of utopia this. If you're a man who likes being near women with their knickers down, I suppose.