The non-secular state education system hasn't turned us all into indoctrinated automata any more than it will turn our children into creationists.
Christians often claim that it has no effect on a child right after they say their child must go to a school that forces them to worship or they will be harmed by the lack of it.
No Christian has ever been able or willing to explain the contradiction.
Also atheists parents when faced with a child who says "But teacher said god/allah is real and we must do what he says" must say "well some people believe that, but I don't".
When the child says "but teacher said so" we are forced to say "Well teachers lie to children".
That's hardly ideal since you need them to trust the teacher in everything else.