How about seeing if it actually happens. Firms like this have other means of defending themselves from openly antisocial behavior and will do it, just like Whole Foods ruthlessly sued the “gay pastor” who faked his cake.
To extend your notion, municipalities and counties should also remove the automatic crossing guards from where roads cross train tracks, because these barriers just might not be necessary. Lets see if "something" actually happens. And if something actually happens, well, let the city or county sue the railroad company. That'll fix the problem.
There are actually good reasons, grounded in human nature, for segregating the sexes in bathrooms, which has been the situation for hundreds, if not thousands, of years. No one needs to conduct experiments to see if the weirdos in the women's room might misbehave.