Writing at Motivated Grammar in 2009, Gabriel Doyle made a thorough and compelling case for accepting singular they as a legitimate epicene third-person pronoun.
After a burst of articles on the subject this spring, the redoubtable Mededitor explored some of the complexities associated with use of singular they in his post "They They My My."
And today at Stroppy Editor, Tom Freeman has posted one of the most thoroughgoing and persuasive treatments, not simply rebutting the familiar arguments against singular use, but presenting further evidence of use by reputable writers and evidence from Google Books and the Corpus of Contemporary American English to demonstrate how widespread actual use has become.
You do not have to like or use singular they; no one is holding a gun to your head. But if, after looking at the articles, following the arguments and examining the evidence, your most considered response is "I still don't like it," then you may want to reflect whether you have the stamina for serious editing.