Data point: I have trained myself to naturally write using third person (their / they / them) in a grammatically ambiguous singular / plural sense. I find if you think about the example you're going to use for ten seconds before you start writing, it is usually possible to start with an example that 'sounds natural' with third person pronouns.

(I did this because someone once, during a discussion about gender and sexuality norms, compared specifying gender to specifying sexuality. I thought, "it would be weird to talk about someone's sexuality unless it was strictly relevant to what you were saying" and then couldn't help finding specifying gender to be equally odd. Here's hoping you find it odd too.)

I still fall prey to using gendered pronouns when the discussion is framed that way by someone else, though.

They probably will, but when they stop to pay more attention they may notice that you used them both in the same sentence, and did the same thing througout your entire essay. I think it works as a reasonable middle ground.

I'm just going off my own experience though. I'm curious if there's a way to effectively test how people react.