When I was a kid I was dismayed to discover that the reason female officers on Star Trek are often called "Mister" was not that the new improved wiser and more decent humanity of the twenty-fourth century had disempowered gender and replaced all gendered titles with a de-masculinized 'Mister' but because it's just naval tradition.
Wikipedia mentions androgyne and genderqueer people requesting the use of a non-gendered title, Mx. to replace Mr., Mrs., Miss, and Ms. I rarely pass as male and don't expect to get Mistered, though I'd like to. I hate "Missus," "Miss," and "Mizz." (In fact, when I read 'Ms.' anything, I think, "Manuscript?")
The trouble with Mx. is that it is unpronouncable. I want to be addressed by a title of respect, not just have it appear on my mail. Mx? Depending on what imaginary vowel you insert, you get "Max Doc" (People would think I am claiming a new first name, not a title) or "Mix Doc" (Not so bad, but it seems to have too much meaning -- instead of being a non-gendered title it seems to say, "mix of man and woman" Doc) "Mux Doc" (A type of online RPG) or "Mex Doc" (Well, maybe, but around here, that'd be "Mexican Doc" and besides, it rhymes too well with 'Keks,' a Scotsman's underwear.)
Any other non-gendered titles you know of, or have invented?