I accept that it is possible to find examples of they/their/them in reference to singular, and in more than just recent works of explicit gender neutrality. This is sufficient to demonstrate that it is not wrong to use these words. But that isn't the same as saying it was right for a work of fiction to use the words - especially, as Bookpossum suggests, 50 years ago. The audience has to be considered.
I mentioned
Too Like the Lightning by Ada Palmer earlier. This book uses they/their/them some of the time. I think it was probably the "some of the time" that annoyed me. I could probably have adapted to consistent use, but there was definitely a strong element of singular/plural confusion that slowed down my reading, and the self-conscious treatment of the pronouns just made it worse.
Because of experiences like that, I'm inclined to prefer "it" as the singular pronoun. The main problem with "it" is that something like "when he carries it" becomes "when it carries it", and so would need expansion to make sense. (We already see something like this in dialogue between two people. When male and female are talking "he said" and "she said" is sufficient, but when two males or two females are talking the attributions needs to be more explicit. The use of "they" will run into related difficulties.) Whatever. It is very much a matter of what we become accustomed to.
Wikipedia has a table of
third person pronouns.