I get that the concept of non-binary (or at least the language used to describe it) is new and scary to people, but it feels like you've rather lost the plot otherwise.
Like trans women just use the same pronouns as cis women, and trans men use the same pronouns and cis men. This is just picking your character's gender same as ever, but now there's a third option for "maybe a little in between."
And while the term non-binary might be a modern concept, androgyny sure as shit isn't, I grew up with Bowie and Prince talking about how they were something other than purely male or female and people weren't as threatened by it back then unless they were incredibly square. It has nothing to do with hormones or surgeries or transitioning or children, non-binary is just people who reject gender labels and norms, which isn't new.