Perhaps we should take a page from our enlightened brethren across the pond. No, not the Brits. The French.
In France, shared bathrooms (toilettes) are commonplace in restaurants, smaller museums and other public spaces. A toilette may have three to four stalls (water closets). The door to each WC is floor to ceiling, so no one can peer under or over.
One or two WCs might be designated for men and the rest for women. Each WC has either a urinal or toilet, as appropriate for the gender designation on the door, and might have a sink. If not, the sinks are in the common area.
Men and women share these toilettes, and no one seems to be concerned about a lack of privacy or being assaulted. Is it possible there are fewer sexual predators in France than in the United States? Or are the French just more practical and not as hysterical about sharing a bathroom as we are? I’m banking on the latter.