Much like with healthcare, all this bullshit with who uses what bathroom is a solved issue in other parts of the world.
... but being an American I assume it will never happen because building bathrooms to respect human privacy and dignity probably costs wealthy commercial property builders and owners at least $1 more than doing the bare minimum required by building code.
The solution, if you're wondering, is that there isn't a giant ladies' room and giant men's room. There are several individual bathrooms, each with its own little sink to wash hands and a real door. It doesn't even take up much space. It's just a short section of hallway with 3-4 doors on each side.

