Well, they're welcome to use whatever word they want. If they want people to understand the when they do so, their options are to either use the existing word or run the risk of having to explain it each and every time they don't.

I think there's a "No binarie" term that's not particularly popular that floats around, from what other comments have said, and it tends to be not well understood by people. It's like the pronouns xe/xer. It probably makes sense if you know the context, but if I just said the word in a sentence people would think I was saying nonsense.