Not only no, but Hell No. They don't, for example, have a "God-given right" to decide that their children need to be educated as terrorists.
What parents really have, is a responsibility to ensure that their childred receive a valid and reasonable education, so that they can properly function in the real world. Not only the kids, but you and I also, suffer if they are illiterate, or so ignorant that they cannot behave properly within our society.
And I notice you didn't answer my question -- which of course you can't without also endorsing judicial activism such as occurred in Roe vs. Wade. But then, you realized that, didn't you?