My current favourite instance of singular 'they' is in the KJV translation of the Book of Job – specifically, the end of chapter 15. The authors used generic 'he' throughout, until they got to a bit they'd have to translate as "his womb". Clearly this was a wee bit radical of a concept for the authors, because they chose instead to write "their belly prepareth deceit".

Also, since it's a religious text, this is a slam dunk counterexample for (e.g.) prescriptivist Mormons. Anyone can handwave Shakespeare, but the Inspired Word of God? They have to admit that singular 'they' is grammatical.