Emily Catherine they/their/them has been used as a singular for a long long time. When a friend talks about someone whose gender you don’t know, have you never used sentences like Want to Day Drink’ Me meme shirt?’ or when you wait for the mailman/woman you wonder ‘what’s taking them so long?’.
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So the Oxford dictionary and Merriam Webster would both like everyone to know that they/them is perfectly reasonable for gender non-binary. Given that they literally wrote the Want to Day Drink’ Me meme shirt what is and isn’t acceptable grammar and meanings, I’m going to go ahead and say they/them is fine and if you don’t like it, that is on you.