Adrian Warnock found the Oxford English Dictionary statement on the use of 'they' as a singular in contexts of unspecified gender:
The word they (with its counterparts them, their, and themselves) as a singular pronoun to refer to a person of unspecified sex has been used since at least the 16th century. In the late 20th century, as the traditional use of he to refer to a person of either sex came under scrutiny on the grounds of sexism, this use of they became more common. It is now generally accepted in contexts where it follows an indefinite pronoun such as anyone, no one, someone, or a person, as in anyone can join if they are a resident and each to their own. In other contexts, coming after singular nouns, the use of they is now common, though less widely accepted, especially in formal contexts. Sentences such as ask a friend if they could help are still criticized for being ungrammatical. Nevertheless, in view of the growing acceptance of they and its obvious practical advantages, they is used in this dictionary in many cases where he would have been used formerly.
Adrian's comments are also worth reading, as is his suggestion as to the best way to deal with one issue in gender translation. The translation he gives of the verse he considers is, I think, the best solution I've seen. It's certainly more fitting with standard spoken English, and it's just about the most common way to say this sort of thing even in the formal settings I often find myself in. Things are in flux with how positively to deal with it (though it's clear that the negative step of rejecting inclusive 'he' and so on is established), but singular 'they' is pretty much accepted in formal contexts enough of the time that I'd say it's grammatical not just in informal English.