Ah, the ever-present debate: Is singular they/them grammatically acceptable?
Short answer: Yes.
And now for the longer answer.
It’s a bit more complicated than this, but use of singular they has been around for centuries. The context is different from how we use it now, meaning that probably very few if any English-speakers were using they as a personal pronoun. It’s safe to say, though, that this contemporary use is born from the long history of using it when gender is unknown or irrelevant. For example, “Someone left their umbrella here...