Call me a fogey. Call me a prescriptivist. Call me a pompous prick. But I still routinely flinch at the use of plural pronouns to signify gender-neutrality where singular pronouns are required. ("If you have a friend in trouble you should help them.") The correct generic pronouns are he and him. (I learned this lesson long ago from a female English teacher.) If you are uncomfortable with the practice, you can use the more awkward he/she and him/her, or simply alternate genders. But I think most people use they and them not for aesthetic or political reasons but out of laziness. Ok, in casual speech I can understand it. I do it sometimes too.
But if the gender is explicitly specified, I cannot tolerate it. Example from a website I encountered recently:
"Every Valentines day you rack your brains for that one special, unique gift that will show your wife or girlfriend [singular, feminine] that you really do care for them [ouch] more than any other."
Update: In multiple posts, the linguists at Language Log have argued the case that singular they is grammatically correct. In this post they cite Shakespeare as precedent and call me a "particularly puristic pusillanimous pontificator" (but not a pompous prick.)
For more on the subject, go here and here.