There's 3 options to take:

1. Ignore their new identity and carry on as before whether it bothers you or not.
2. Slowly easy away from the friendship until it's no more.
3. Talk to your best friend about the new identity, challenge their views along the way, express your concern.

Since you mentioned best friend, I would go with option 3...A best friend in my mother's country is someone you are very much close to, it's like another sibling you tell everything to and can be open and honest, they are basically a part of your family.

For your best friend, I would ask her/him "Why do you feel you are non-binary?". If she/he say "because I don't like [stereotypical feminine/masculine thing] or I don't fit in [feminine/masculine role]", ask them if that stereotypical thing(ex. makeup or sports) makes a "man a man" or a "woman a woman". Challenge her/his thoughts. You don't necessarily have to share your thoughts/perspective right away, you can ask it in a way to "better understand" him/her. Plant a seed in your bestfriend's head. Ask her/him why she/he thinks the way she/he do.

Your bestfriend may very well no be TRA, but just read about non-binary and went "Huh, this describes me". Maybe the word your bestfriend was really looking for is "gender non-conforming".

Talk to your bestfriend and gauge her/his thoughts. If she/he does happen to be TRA...That's OK...She/He is still your bestfriend, the most you can do is just be there for bestie and keep talking to bestfriend. [Edit: Just wanted to add though, if she/he becomes toxic towards you, then it's okay to separate. Don't make yourself suffer. That is your bestfriend's loss for losing someone who cares about her/him.]

My younger brother was in a cult for about a year or two and snapped out of it. It was not easy.