> A much more reasonable (non-fear mongering) approach is to use the gender the person identifies with.

The problem with /that/ would be that non-transgenders would possibly feel uncomfortable with that - which I believe, but correct me if I'm wrong, is why there's gender-segregated bathrooms in the first place.

The only solution would be, as the other commenter says, to only have unisex bathrooms and to tell anyone that complains about that to fuck off.