Americans are so spoiled that everyone must share multiple-toilet, multiple-urinal bathrooms. If America didn't build such multiple accommodations, there wouldn't be any issue on who can go into the bathroom with whom.
Elsewhere, there would be single-toilet and even without a urinal for each bathroom facility. People line up or take turns and on two persons are ever there at the same time, except perhaps a parenting assisting a toddler.
And then there are those countries where people just run into the woods. There's no label of which part of the woods is male only or female only or otherwise.
But the American debate is valid in a few minor instances: we have been conditioned to separate the sexes in the bathrooms, and people are uncomfortable having someone different in it while they are supposed taking off their clothes or part of their clothes; in instances where there is only one woman in the bathroom--with this gay/lesbien right these days--the transgender might take this opportunity to sexually assault that solo woman; and privacy intrusion is a big concern for many--people just want that place to be as private as possible, since it is a "special place" for a specific purpose.
With freedom reining so wide these days and people's ethics and inclinations becoming less strong against it, it sounds like the shared bathroom is going to become a permanent reality. People don't see any problem having someone of two different sexes in the same bathroom at the same time anyway, since people these days marry the same sex without embarrassment or shame or even just timidity. Some feel it's just a cool thing.