> My usual reaction when people refuse to use pronouns such as "they" is that they (hah) don't want to acknowledge gender identities outside of the male/female binary.

This is probably different. I for one don't think there are enough non-binaries out there to warrant a generalised pronoun, let alone its generalised used. I believe even most trans people identify as either "he" or "she".

On the other hand, I like to maintain uncertainty whenever someone's gender is either unknown or undisclosed. When talking about a hypothetical individual for instance, being able to refer to them neutrally is convenient. On the other hand, I hate to use "they" whenever there might be a number ambiguity. In those cases, I'll use "he" or "she", or find another phrasing.

Finally, gender-full pronouns are pretty good at disambiguating roles without having to repeat people's names all the time. Crypto examples with Alice and Bob for instance benefit from saying "he" and "she", so the audience (or student) readily understand whether we are talking about the initiator or the recipient.