It is both. The primary job falls to the parent. But it's the parent's job to ensure that the public school teacher who is entrusted with the kid 5 days a week demonstrates good morals.
If the parent fails to do this, they are failing to ensure that the kid is taught appropriately. That is too much time away from the parent not to ensure that they have good role models during that time.
"but your activities inside the classroom (at least what you've shown here) are more reprehensible than theirs. "
Oh yes, studying the Declaration of Independence is reprehensible. Giving them all the facts and teaching them to think critically about evolution is reprehensible. I'm soooooooooo dangerous!!!!
Bull hokers Mr. "It Takes A Village", you only have what privileges I grant you as far as my kids are concerned, and that's not one of them.