You could tie it in with letting the user specify the name to display; changing away from using Twitter handles is probably not a bad thing anyway. Thus you could have as part of the sign-up process:

    1. Call me _________
    2. Refer to me as 
       ( ) male ("he")
       ( ) female ("she")
       (x) gender-neutral or plural ("they")
       ( ) actually, we're a group ("they")

For e.g. Twitter sign-up, you'd auto-fill the first with their username and the second with gender-neutral.

That does sound rather awkward and could hopefully be improved upon. (I added the final option as it occurred to me businesses could use this.)