"Someone dropped his, her, their, nir, or xir glasses" just sounds like you're taking the piss. "A pair of glasses have been dropped (by someone)"?
I've met a lot of non-binary people, but I've never actually met someone who prefers nir or xir. The most common pronoun by far is "they", followed by "I don't really care about pronouns", followed by "just pick whichever you feel like". I feel like with a few exceptions and edge cases, these are straw-men pronouns trumpeted up by TiA users to mock others.
I know someone online who prefers xir, but the others just wanted they/their or didn't care. I didn't even know nir was an option.
I think people IRL tend to go for the pronouns they think will be easiest for people to use vocally. The only person I know who prefers
ne is a Canadian.
They is a perfectly common singular pronoun in British English. It rarely leads to ambiguity and can always be fixed by rewriting the sentence.
Edit: Btw, I have no idea what TiA is. I literally got a load of medical web pages and urban dictionary told me it was some really cool girl.
Also, it's the morning of the 6th - is Donald a 6am riser? If so, it'll be very soon.