I don't think a third category is a good idea but, to be fair, I don't see any particular reason that passports need to be gender specific
at all 
. Their photo ID technologies are very advanced these days, specifying gender on the passport is sort of an irrelevance these days. It has your name, D.O.B and photographic identification (and I believe other stuff on the microchipped ones) so why gender is needed as part of the info, I don't really know.