When I started interacting with a non-binary person more often, the only reflexive pronoun that came to mind was ‘themselves.’ As in, “They bought themselves a pair of socks for their birthday.” It felt a bit awkward since I couldn’t shake the plural association in my head, but I still used it to be respectful.
Then I remembered that the word ‘themself’ exists and I felt stupid.
That's something I wonder about as a non native speaker: it's singular they but verbs are still plural (they are, not *they is, they comes). Maybe this will change some day, maybe not. Singular s might die out anyway or maybe because of singular they.