I have a partial solution for single-gender facilities that no one will like. (Not a solution to "who's a woman," just one narrow issue). It involves observing privacy etiquette when possible. I realize in some cultures it doesn't matter to anyone, but I'm not talking about them.
I would post notices in locker rooms saying this is a single-gender facility and asking people to respect communal modesty. Also include a way to reach staff members if stakeholders feel they must report problem
behaviors. I wouldn't necessarily list all the behaviors, but examples would be available in writing and they would be based on what people do, not who they are.
In itself, this process may feel like a violation of some people's rights, but it does accommodate a variety of concerns. Everyone gives something up; no one gets to have everything they want. Facilities managers would need training in how to manage complaints, or perhaps this would be outsourced to specialists in mediating gender issues. Behavior accepted by everyone would not generate complaints.
A lot of people are shy and IMO it's just good manners not to either gawk or gratuitously flash body parts. My experience with group nudity is: As a young girl I had sex-separated PE with open, communal showers. I wasn't crazy about it, but there might have been value in seeing a variety of bodies. As an adult, most women I saw in locker rooms seemed to have a middling acceptance of partial nudity. If I'd been swimming, I would want to rinse my suit off as well, and the showers had partitioned stalls with hooks or benches. I'd rinse off, then wrap a towel around my waist or my body and finish the drying-off, hair-styling or makeup-applying routine at the sinks or by a locker, without either obsessively covering my body or going out of my way to flaunt it. I wouldn't, for example, set up camp in a middle bench and ostentatiously air-dry my private parts. I might use the locker door to create a visual privacy zone.
That may sound unreasonably prudish to some people, but even when traveling with a female friend, we both seem to observe such etiquette. Now I live with my mom, and we both seem to follow the "rules." But I had an aunt and cousin who routinely took off their tops and bras when home alone (with each other, I mean). I much prefer not to be fully dressed when I live alone. Partly to keep pet hair off my clothes