There are two genders. There are some people who biologically don't really fit into either.
"androgynous", "bigender" and "gender non confirming" are not genders and no one should be referred to be ze/zir/zirself pronouns.
I get how the made-up pronouns are silly (although to be honest I've never heard an argument in favor of them) but I don't see what's wrong with calling yourself bigender or whatever.
TBH the term "bigender" sounds weird and completely nonsensical to me. Not that it matters, of course, since whatever labels people choose to identify themselves with makes absolutely no difference to my life.
I mean, if people feel that "bigender" is the best word to describe them, I don't have a problem with that.
I can understand getting annoyed at people who expect others to address them by pronouns other than he/she/they, though.