The whole latin-x thing is a bit funky, though, because the entire language is gender-based, every noun being either male or female. Then again, I suppose the issue is mainly with words used to refer to people, like a mixed group automatically being referred to using the male noun. The rest of it is fairly arbitrary, maybe.
Does Dutch have gender?
But yeah, they and their are used all the time with a singular meaning. I actually think they is more "felicitous" than he or she, which sounds clunky. Themself looks awkward, but as the author points out it'd become normal over time. Really I can get behind this usage of they, even as someone with reservations about the profusion of gender identities.