In principle, I'm not sure what's gained by giving parent the power to indoctrinate children in their own convictions.

Except that your wording would allow parents to fight a state school teacher who peddled prejudices not based on evidence in a science class.

Private schools are, of course, a different matter. If you don't like sectarian teaching don't take your child to a sectarian school. Which is why those kinds of legal protections of parent's rights to a particular kind of education for their children imply the need for state schools where the appropriate teaching is delivered.

If you are not convinced, try it on someone who has not been entirely debauched by economics. — Piero Sraffa