If I have to share a public bathroom while I am in it, I prefer it to be a men's room, not a mixed-sex loo. But many establishments in New York have two bathrooms, each with only one toilet, and a door that locks, but still sex segregate them. This clearly costs patrons either time or embarrassment: occasionally "your" bathroom is occupied for a while when you need to go, while "their" bathroom is not: then, you either fidget with an unused toilet a few feet away, or risk plunging into the "wrong" bathroom, and getting a dirty look when you come out to find someone is upset that you took "her" ("his") rightful place in line.
So why does this practice persist? I considered the idea that people don't like even serially sharing a toilet with strangers of the other sex, but that doesn't seem right: Haven't we all done so repeatedly, since we were children, every time we've gone to a large party in a private home? Why would the fact the building says "restaurant" on the outside suddenly make us go all squeamish?