So here’s a fun fact: a lot of people who don’t identify as a binary gender don’t use binary gender pronouns.
So what to use instead? There are hundreds of alternatives, often depending on language, but since I am writing this in English, those are the ones I will focus on.
Singular ‘they’ is one of the more common ones you’ll come across. It works exactly the same as if it were being used in the plural.
“I asked them if they enjoyed themself, and they said they did.”
There has been some push back on this one, because there are people out there who will try and tell you singular they is grammatical inaccurate. Those people are ridiculous.
More on singular they at this link.
Ze and Hir
These should hopefully be pretty obvious: they’re compressions of “he ” and “she, and”his” and “her”respectively into something that is both and neither, and so can cover a lot of genders. They’re used in the same way as he/she and his.her, and takes -self in the same way.
These are most often used by people in the genderqueer, but they are not exclusive.
“I asked hir if ze could pick it up on hir way home, and ze said sure.”
Some people forgo gender pronouns entirely, and would prefer people to use only names when talking about said person. This is totally fine, and may feel strange to begin with, but is worth making the effort to do.
As with so much of this gender stuff I’ve been writing about, personal preference is important, and it is becoming more commonplace for people to introduce themselves with names and pronouns, for con badges to have stickers with pronouns displayed, and other little ways of making things more inclusive of non-binary gendered folx.
Language evolves all the time, and it’s a small step to take to make the world more inclusive.