Most traditions or cultural values don't demand belief, unlike religion.

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, even if there's no mysticism behind it. Are you going to arrest parents for teaching their kids that dessert is supposed to be eaten after dinner?

Because we as a society have decided that these are the values we wish to protect and propagate. We have made no such decisions with regards to religion, in fact likely the opposite.

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.

, in fact likely the opposite.

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

I just pointed one out.

You did not. You gave no logical framework that justifies state violence in cases of religion and doesn't justify it in cases of non-religion. Your response to me pointing out that believing in God and believing in human rights can both be affected by your position was "but one is rightthink so it's fine," not any kind of logical distinction.

Nobody's advocating indoctrinating them into wearing skirts. I don't see anybody protesting them wearing pants or w/e.

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?