I fall rather squarely into the prescriptivist class of grammarians (as opposed to the extreme corpus linguists who seem to feel that language is entirely fluid and dynamic and should be bound by no rules whatsoever), but find it perfectly acceptable to use the third-person plural forms for persons of indeterminate gender or identity. While it has often been taught that using the 3rd person plurals in that way is incorrect, there are a number of pragmatic and historical reasons why it isn't so. A couple:
1.) It is readily understood by native speakers; we've been doing it that way for a very long time! Shakespeare, Chaucer, Jane Austen, Samuel Taylor Coleridge, George Bernard Shaw, George Eliot, Elizabeth Bowen, C.S. Lewis, Oscar Wilde, all have used 'them' as an indeterminate singular pronoun.
2.) It fulfills a need. Using 'he' causes an assumption, as does using 'she.' Some authors choose to alternate between the two, but that is just confusing. Saying 'he or she' and 'his or her' every time is far too wordy and cumbersome. Considering that English only has a neuter third-person plural, 'they' is a perfectly good stand-in. (Heck, the Germans use 'sie,' 'sie,' and 'Sie' (her, they, You) without any issues. Aside from some fun and intentional linguistic wordplay, ambiguity is resolved through context.)