As a grammar nerd, I call bullshit. "They" as gender-neutral singular pronoun has been part of the English language for centuries, and it's only in the last hundred years or so (give or take a bit, I don't have time to look it up right now) that prescriptivists have started freaking out about it. Yeah, it's a little awkward, but modern English NEEDS a gender-neutral singular pronoun, and "they" is the best we have.

It was good enough for Shakespeare, and it's good enough for me.