But plenty do. Everything from "this is how dish A should be eaten" to "leave your shoes at the door" to "we should be nice to our parents" is a belief,

They're a belief. They don't DEMAND you belief in them, else go to hell / get isolated by your family.

Are you going to arrest parents for teaching their kids that dessert is supposed to be eaten after dinner?

Is anybody discussing arrest in the current situation? You're pulling a classic reductio ad absurdum.

So parents should only be allowed to teach rightthink, and the state has a duty to use its monopoly on violence to intervene whenever parents attempt to teach children wrongthink (wrongthink being anything other than what the state, representing society, has deemed as rightthink). You just trampled all over freedom of thought and conscience with that statement, and PS: Fascists can use the exact same line of thought to ban pride flags and minority cultures.

This is not an attempt to ban parents passing their religion on to their kids, it's merely preventing them from doing so in school, and giving some children potentially their only taste of gender equality that they'll receive before they turn 18.

Yeah you're gonna have to back that one up with numbers.

You've made a lot of claims yourself, feel free to back them up any time.

In many societies schoolgirls are, in fact, expected or forced to wear skirts rather than pants for school (see: Japan), and as for the rest: Why do women wear women's clothing rather than men's clothing if not for cultural indoctrination? Why do men not wear skirts and tank tops if not for cultural indoctrination?

We're not talking 'many cultures'. We're talking about Sweden, and last I checked they did not force girls to wear skirts. For the record I'm against forced uniform segregation by gender.