So many pronoun problems among GRADUATE students that I had to blog about it. I hope it'll save me time later.
They is also generally accepted as a gender-neutral singular, and is generally the preferred pronoun of many gender non-binary people.
I have actually been taking it upon myself in the last few months to substitute they wherever possible when a gendered pronoun occurs, because I would like to break down the usage of assumption of gender or placing a gender on someone that may be incorrect.