Um, okay? So there are "unisex" bathrooms in the White House? Most houses have unisex bathrooms. I've never designated my household bathrooms by gender, nor have I heard of such a thing. Some stores lately have unisex restrooms available with segregated bathrooms.
I simply don't see the likelihood of any implied "unintended consequences" as happening, at least not in a manner that couldn't be easily taken care of with other laws.