Hi, OP here
I'm not a troll, I just haven't been back to this thread since last night because a) I've been teaching all day and not browsing Mumsnet, and b) when I finally got home from school I was so knackered I fell asleep under a cat! Finally got a chance to look at my phone and was staggered to see how much the thread had grown in my absence!
Having read through the whole lot, I can see that most comments broadly agree with me that parents claiming their 9 year old daughter is non-binary is frankly ridiculous and potentially damaging to their daughter as it will confuse her as she heads towards puberty.
Far better in my opinion to explain to her that it's absolutely fine not to be a "girly girl", that sex stereotypes don't have to be abided by and that she should challenge any of her peers who say, "girls can't play football," "girls can't have short hair," etc. Far better to provide her with examples of strong, talented women excelling in careers and activities which have traditionally been male-dominated. Far better to teach her that as a woman she can have any hairstyle, clothes style, career, hobby, friends etc and she shouldn't feel her choices to be limited by her sex. She's a very bright girl who is very interested in a hobby (not sports) which is quite male-dominated.
She may turn out to be lesbian or she may be heterosexual. What she won't grow up to be is a male, or a person of no gender. And personally I think it is dishonest to confuse children by teaching them that something untrue can be true. As a teacher I can challenge sex stereotypes in the classroom and give the girls examples of strong female role models. It's not my place to sit down with this girl and tell her her parents are wrong, and I won't be doing that.
As I said in my original post, I will be calling her by her name in place of using they/them. If one of the other children refers to her as "she" or "her", I won't be telling them off and telling them to use they/them.
I won't be shouting at this girl that she's being ridiculous and pointedly saying SHE and HER loudly in front of her to embarrass her and make a point (some misguided poster on this thread appears to think I'll be doing this). That would be abusive, unkind and unprofessional.
I will, in fact, be treating her very kindly because I feel very sorry for her that her parents have decided to take this course. I hope as she gets older she will be able to see her way forward more positively.
I would like to thank all the posters who have made thoughtful comments.