Mara, I’m going to tell you slowly, and you’re going to have to take this in:
Non-binary is not one gender, or feeling “in-between the binary”, or “outside the binary”, or anything that you’re currently thinking. It is not androgynous. It is not expressed in one singular way.
Women are female. They are one gender, one shared experience of their own being. Non-binary people are not.
Non-binary people are not one gender. You cannot - CANNOT - group them under one pronoun, in a fantasy world or reality.
This would be preventing, or at least discouraging, the freedom to present individually as a non-binary person, by removing someone’s ability to use the pronouns, or be respected by the pronouns, that they have chosen.
To do that is non-binary erasure. It would be erasure in reality, it would be erasure in fiction, it would be erasure anywhere. You would be actively contributing to the erasure of non-binary people.
Non-binary people have been known to make up their own pronouns where the language does not help them express their identity.
One set of pronouns does not fit all people and all genders and never should, neither should one set be considered “correct”.
I’m warning you very politely, Mara, that you should not impose your cis experience of gender on non-binary people in your game when actual non-binary people are telling you that doing it would make them uncomfortable.