It has NOTHING to do with prohibition, unless you think men dropping their trousers in the ladies’ room is as harmless as drinking a glass of wine. You do seem to think that, which makes you a flaming leftist who should GTFO of our party.
How old is the entire concept of a public gender room? Not much over 100 years at most.
Think of how the Founders would have looked at this. They would have laughed and said, re-architect your rest rooms!