I’m gender critical but I am also interested in grammar and language evolution.
“they”, “them” and “their” is very well established in English when the sex of the person is not known or one is talking about individuals from within mixed group “If anyone asks, tell them they can buy water in the shop across the road” or “the owner of that car needs to come back and collect their bag from inside”. Totally normal.
I’ve actually noticed that my 8 year-old will default to using “they” even when he does know the sex eg “Who was that you were playing with today?” “That’s Daisy, they joined the school in Year 2”
(Daisy is entirely binary and has no issue with being called “she”).
It’s an interesting linguistic evolution and he’s not doing it because he’s had any indoctrination about trans ideology. Funnily enough it’s very much the opposite, gender and sex matter so little to him that he doesn’t feel the need to highlight it in his language.
To answer OP’s question, I actually think that non- binary is something that it’s fine for a teacher to model and a little kid will just learn the person’s name and go with it, same way they’d have to learn a tricky pronounciation of Balasubramanian or Llwellyn or MacInnerny. What’s the difference between a teacher wanting to be “Ms” (“Miz”) instead of “Mrs” even though she tells her class she is married? Is that “denying reality”?
On the other hand I would disagree with a male to female trans teacher wanting to be called Ms, Miss or Mrs as that is using a label assigned to people of the opposite sex.
No issue with a teacher whose ideology is that sex and gender are irrelevant to how they live their life, as long as it is not preached in a heavy-handed way and kids are not punished for using a gendered title by mistake.
Lots of issues with a teacher who tries to convince kids they have changed sex.