It is and has been since roughly the 14th century. Although, it's apparently a subject of contention amongst grammarians (plural vs singular).

https://www.etymonline.com/word/their

There are lots of things from 14th century English that are no longer used today. Language evolves.

Singular “they” has been considered an error for a couple hundred years.

I see you're on the singular side of the contention amongst grammarians (plural vs singular). I think you're wrong as do a lot of other people. The fact it's been used widely in this context for the past couple hundreds years proves you wrong.

> The fact it's been used widely in this context for the past couple hundreds years

Citation needed.

I already provided one. Where's yours?

~600 years of historical English usage disagrees with you [1].

[1] https://public.oed.com/blog/a-brief-history-of-singular-they...

There are lots of things from Old English that are no longer used today. Language evolves.

Singular “they” has been considered an error for a couple hundred years.

Your source cites usage from the 1300s. It says nothing about the last couple hundred years.