10 year old non binary friend

The Ken/Spiderman stuff would be fine if it was just random chat, but in this case she's repeating common themes and it indicates she's been immersing herself in on-line nonsense and it's just going to escalate.

If the parents chase you up about the friendship cooling, which is quite likely based on the parents I know who get themselves so involved in cheerleading this and looking for victimisation, just say they have different interests now. Don't get into telling them their daughter is a girl or asserting what pronouns you are going to use for her, they will love that. Instead just say it's all a bit boring and sexist and change the topic.

My DD distanced herself from all the kids who were doing this in her last two years of primary. The one that sounds most similar to this child just kept upping it to get more attention, switching back and forth to make sure she could keep telling on people. She has no friends now, it's too much like hard work.

I agree with this. You don't have to accept the invite in to the drama. That said if your DD no longer wants to be friends with her then that's that.

If it were my DC I'd be telling the teacher that little X might use they/them pronouns for herself, but she can't force the rest of the class to use them for her and my DC will be using sex based pronouns as is their right. X's wants don't trump everyone else's.

This is discrimination towards ND kids,kids with English as an additional language, kids who don't believe in gender woo, and frankly just kids who've got their own shit going on and don't need the mental effort of making special efforts to remember little X's special specialness. This is how we get social contagion, other kids see the specialness and fancy being special too.

But then I'm a pissed off middle aged woman who's had enough of this shit, let alone in primary school, so yeah.

"is obsessed with insisting spider man has a boyfriend and told my daughter Ken as in barbie and Ken has a boyfriend"

I have no idea about Spiderman but she could be right about Ken and not the first to propose that theory

Your daughter doesn’t have to be friends with anyone she doesn’t want to, certainly not one who is bullying her like this.

🤣
In that case I'll stop overanalysing your grammar, sorry!

for the children forced to pretend their kid is the opposite sex to reality.

Or in the case of a 'nonbinary' are they pretending the child has no sex at all? who does this kid change with for PE ?

Yes OP, but you've got a really confusing mix of singular and plural object/verb agreements here:

My daughter has decided they no longer want to be friends with this child as they find the whole thing extremely confusing and overwhelming and is sick of the child running off to tell tales to the teacher or her mum if my child refers to her as 'she' and not 'them'.

I don't blame you for sticking with "my child" at the end just to simplify things!

I'm not having a go, I can't imagine how hard it is to be a parent nowadays (I don't have that problem!). I'm just thinking you might have become so conditioned to oversensitivity that you're unconsciously reinforcing the confusion.

Otoh using a mix of correct sexed pronouns or 'they' for all and sundry may serve to deflate the 'special status'.

My daughter has decided they no longer want to be friends with this child as they find the whole thing extremely confusing

Don't you feel safe referring to your own daughter, in private, as "she"?

Parents must show where the boundaries lie, and if you are tiptoeing around rules laid down by extremists, then perhaps this feeds into your daughter's confusion.

This kind of thing boils my blood, why should any 10 year old child be compelled to go along with this? The parents clearly just want a special rainbow child.

As far as I can tell the parents of children who identify as trans dgaf what the impact is on other children.

We see it so often in the parents of trans girls. They particularly don't give a fuck that our daughters are forced to lower their boundaries by accepting these boys as 'girls'.

It's no great surprise that this child has few friends. 10 year olds should not be subject to "pronouns" and getting snitched on to the teacher if they call a female she/her.
I would be having words with the teacher

Not correct.
It needs to be more like these are the facts and I/we believe in facts. Some people believe other stuff; they are entitled to believe that other stuff but you don't have to consent to go along with it - just distance yourself.

My DC had to sing hymns to God praising him for making the world. Then they had science lessons with evolution. So there is a historic culture in this country of ‘this is what some people believe in but we don’t’. The thing I would say (which is annoying but gives your Dd an easy life at her age) is tell Dd not to discuss it with her. You can just about get away with telling a religion teacher that you are atheist but with gender ideology it’s a step too far.

Sorry but I would not go for “some people believe this but we don’t …”. It gives equal legitimacy to the other view.
It needs to be more like, these are the facts but some people are confused and believe this…

These poor children. My concern would be to what extent this is being enabled by the school? They can be very powerful in either a dangerous way by fawning over and centring this nonsense or they can calmly acknowledge a child's confusion while focusing on their core role - the learning and social / emotional development of all the children.
I'd have a discussion with the school - maybe the class teacher unless your DD suggests they're part of the problem in which case, speak to the Head.

So young.
Your DD should treat this the same as if she had any sudden difference of opinion with a friend. They can agree to disagree but if it becomes a point of conflict, she needs to step away from the friendship.
Teachers will want other pupils to use preferred pronouns because that's what they have been told to do.
At 10 she needs to have an understanding of sex and gender and if you don't talk to your kids, tiktok will fill in the gaps. But she doesn't need to feel overwhelmed or upset by it - working out how you feel about yourself is very much a part of growing up. But feeling 'like a boy' or 'like a girl ' based on stereotypes is not an indication of whether you are one.

I feel sorry for the 10yr old who is seeking attention and unwittingly driving any potential friends away. Absolutely support your DD in withdrawing from this girl. Tell your DD to interact with her as little as possible.

If you ever speak to the parents of this girl, I’d do the faux sympathy/understanding and sympathise that poor ‘Alex’ hasn’t realised that we don’t have to comply with regressive stereotypes or label ourselves by how much or how little we fulfil them. Tell the parents that perhaps that’s why their DD is short of friends, then hopefully the idiot parents will stop manipulating her into this - which is what they’re doing by the sound of it.

My daughter has decided they no longer want to be friends with this child
Your DD is entitled to decide that this friendship has run its course.
Nobody has to be friends with anybody. Maybe it's time to have a (?another, ongoing?) chat with DD about consent?