Thinking this will just become a boy/girl split

I would sign my child up to the one they wanted, I don't care what other people say unless you are forced not to chose then the pressure is self inflicted

So your daughter is getting the choice to do ballet or karate and that's sexist!? How? Your 4 year old daughter has chosen ballet of her own free will and that is sexist!? How? She already does ballet outside of school but that's not sexist I presume?
You say your 4 year old hasn't yet started at the school. So how has she been pressured into doing ballet by the other kids? Has she even meet them yet?
Girls on average prefer ballet to karate. Do you think ballet is a lesser sport to Karate? Because if you don't why is it a problem? I'd understand if you tried to encourage her to do karate for variety because she already does ballet outside of school. But it seems you think karate is the better sport for your daughter because boys are more inclined to pick it.

Following term dunno why I typed year there!

At that age both ballet and karate are surprisingly similar, both require balance, poise leg strength, and a certain amount of mindfulness. I mean in an ideal world you'd do one for a term, one the following year and pogo sticks in the summer term, but both ballet and karate build excellent skills. You can always find a class outside the school day in either disciplines, so I don't see a major problem here.

I agree with you. I think they should both have the opportunity to do both.
It's pretty sad tbh that they're already socialised so strongly but that is the society we live in.

How's that the same? It's telling people they can't do something they want and have to do something someone else thinks they should.

It does seem poor to not introduce both activities to all children (whether that is a year of each or alternate terms or whatever) , so that children can actually make a choice once they know what they actually enjoy.

This!

I think the question here is one of choice - isn’t it just as wrong to say to a girl that she’s got to do a martial art as to say that she has to do ballet?

Don't make such a fuss it's only one class out of the entire curriculum

Why does the school want them to do one sport for six years? I'd hate to still be doing an activity I chose in 2017 with no idea if I'd like it or be good at it, and I'm a lot better at thinking through choices than a four-year-old.

It's odd that they don't let them try both or change, but you might be surprised at how mixed the classes are. My son opted to drop football and take cheerleading and he couldn't be happier. There are quite a lot of boys with him in the class!

If your dc already does ballet it's prob best she did something different. I know several young girls who do karate or other type martial arts and would hate to do ballet.

It isn't being delivered in sexist ways though is it? All that's happened is the parents have been given a choice. It also sounds like all the other sporting activities are mandatory so I can't see any issues in them delivering an "equitable education." If OP is so bothered about it she can petition other parents to choose the less expected option.

It isn't sexist for little girls to choose ballet. It would be sexist to force them into ballet just because they're girls. By claiming it's sexist it's erasing the girls' voices, letting them know what they actually want to do isn't acceptable and they should do the opposite.

So you would have rather persuaded your dd to do karate when she had a clear preference for ballet? Why?
Surely trying to persuade her, for a whole year, to do something she didn't want to do (and a lot of children would have changed their mind to please a parent) for what reason? Doesn't sound like the reason is you'd think she'd actually prefer it.

I did karate as a child (but not ballet), my ds has done ballet, tap and jazz (but not karate), Dd did Taekwondo and ballet. It was our choice, not a parent wanting to make a point.

You're the parent though.

Have you missed the fact that the op is talking about a curriculum activity? Do you think a school curriculum should be delivered in sexist ways?

I would be concerned about the school's ability to deliver an equitable education.

What? Like maths? Or geography?

Maybe we could just have all the boys do STEM and the girls home ec?

So by that reasoning why don't you have your daughter do karate regardless of the fact she wants to do ballet? Seems like you're annoyed the sexes will fall into the two categories in a stereotypical way but you're encouraging that by your daughter doing ballet anyway.

"In the email they asked that parents/pupils pick either Karate or Ballet for the school year."

You really think the 4 year olds are calling the shots in this scenario?

It's a curriculum activity, it shouldn't be delivered in a way that descends into reinforcement of sexist norms. Just rotate it around equitably, the same as they plan all the other curriculum activities.

It's terrible children are doing things they like and you'd rather they were made to do something they didn't want to just to look good?
Would you go to a adults pilate class and tell them, 'no more! Next week you're doing muay Thai for 6 months,.like it or not!' ?

Sounds ideal.