Grammar changes, but there is still a question of implication in the meantime.

If there is a problem with "they" as a gender-agnostic third-person singular, it's not that it's a perversion of grammar because (1) English has had it before, and (2) it's not like English grammar isn't full of other weirdnesses. For more on the lack of historical justification for opposing singular they, see https://blogs.illinois.edu/view/25/677177

If you wanted to argue that it, too, is slightly depersonalizing to the people that you apply it to, then maybe you'd have something.