“But of course you should be allowed to home school.”
I quoted that part, because of course you should. If they want to make sure people know stuff they can have general exams that need to be passed. That I would not object to.
But to your larger point, I totally agree. And I remember my mother saying (this would have been in the 1930s) that every day she and her brother would come home from school and say what Sister had taught that day. And every night her father would bang his fist on the table and explain why Sister was wrong.
Kids don't know what they're learning may be wrong so the have no 'red flag' experience. They simply hear adults telling them how and what to think without question.
So the teacher says, 'Communism is great!' and they believe it to be true.
That's why parents are constantly being shocked. They're not asking their kids what they're learning.
Simply asking, 'what did you learn in history today' or 'what novel did your teacher give you to read' would go a LONG way to circumvent public school indoctrination.