A: Somebody called asking for you.
B: Oh, what did they want?
This has always sounded perfectly natural in colloquial English (at least in the US; I can't speak for other countries). Contrast with the following:
A: Joe called asking for you.
B: Oh, what did they want?
This construction is slowly becoming more widespread, but would have sounded absolutely bizarre and ungrammatical to most native speakers (regardless of literacy/education) before the movement for gender-identity inclusiveness became mainstream, because people didn't really conceive of the possibility of knowing a specific person but not being able refer to them as "he" or "she".
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In response to sibling comments: I think this explanation is a lot more convincing than any variant of "singular they is (or was) wrong". There are two very different kinds of singular they, which elicit very different grammaticality responses from native English speakers.