Teacher asked DD how she IDs

Complain.

It's inappropriate to single your daughter out in this way.

I would complain.

Please complain OP.
Until teachers like this are challenged about imposing their niche belief in sex change on children, they'll continue to impose this dangerous to the young political ideology on children in schools. Children are too young to understand or negotiate all the dangerous aspects of this and it's just wrong that adults in authority are allowed to behave like this.

I had to look up what the “ blue and pink flag“ meant. I am actually gobsmacked that a teacher can signal and promote their sexual politics in school in this way. I’m really shocked. The fact that the teacher was also questioning your daughter about her sexual identity is also out of order. (It’s so intrusive, creepy even). I would say something to the school. Unfortunately, my experience has been that over the last decade or two some teachers take it upon themselves to promote various politics when they really have no business in doing that. My son’s friend’s secondary school had huge Pride banners erected over the entrance to the school a few years back.

If the teacher buys into gender ideology they'd be outraged at a pupil who said they are trans being asked, are you sure, have you ever ID'd as your birth sex?

Can you imagine the reaction?!

If it's not an acceptable question one way, it's not acceptable the other way.

No debate. Innit.

I do, in all seriousness, think it would be reasonable to raise with someone that DD was upset/mortified that she was questioned publicly on her gender identity and that her first answer wasn't accepted.

OP, you should start a crowdfunder to sue the school - this teacher needs to be disciplined and ultimately fired.

I'm sure lots of people will be more than happy to support you with a little gardening.

"Gender woo, sweetheart" I have no idea what you mean by this. Can you explain please?

Apart from anything else it's a very personal topic and not one that a teacher should be prying into. It's similar to asking whether she's ever been attracted to women. If your dd brought the subject up and wanted advice then it might be appropriate for a teacher to listen to her concerns before signposting to the appropriate source of info / help.
But for a teacher to ask such personal info without context and in front of another student, is completely out of order.

It's worth a complaint simply because your daughter was upset. I would also ask the school to make the teacher apologise to her.

I’m not interested in hearing your gender wooo sweetheart

Well yeah if your DD was embarrassed by it I’d complain. Ridiculous nonsense to question her like that just for not looking sufficiently “girly”.

Oh for God's sake really? Where are you going with this?

Well said!

This! Not a teacher but I did mistake someones 13yo DS as a girl last weekend, probably due to the long hair and not getting a great view. She (mum) just politely said he not she and that was that.

It would be if she wasn't living in a world that also houses fuckwits like the teacher mentioned in the OP.

That’s my point. The OP said

but has always been very clear that she's a girl.

I want to know what she means by that. Surely biology is enough 🤔

Long past time for the grown ups to kick to bullshit that’s “misgendering” into touch.

She exists as a female human being. What does she need to do to make it clear, why does she need to do anything? She is a girl because she was born female, the assumption should therefore always be that she ‘identifies’ as a girl.

My DD is a tomboy - short hair and trousers all the way - but has always been very clear that she's a girl.

What do you mean by “has always been very clear that she's a girl”?

Other than being a biological female what does she do to make it clear?

I agree. No ideology should be touted in schools. And genderism is a harmful ideology, from gaslighting children to abolishing women’s single-sex spaces to letting male sex fetishists give intimate ‘care’ to elderly women.

Perhaps the teacher was erring on the side of caution given that people have found themselves in all sorts of shit "misgendering"