One of the things Abraham Lincoln pushed was public education.
I will have to admit when I was in public schools in the 50s and 60s we had no really bad indoctrination. We had Bible reading every morning and said the pledge of allegiance. We were taught patriotism, decency etc.
The problem tho is that they have your children for a good part of their lives and if they want to they can and now do, try to turn them into little communists.
First time I was really aware of indoctrination was 8th grade, in 1973. That year they got rid of “History” and replaced it with “Social Studies” and we learned about class warfare and situational ethics. They didn’t use those terms, but I knew they were up to something, and I eventually figured out precisely what.
There is a difference between “public education” in its classical American sense of locally controlled, publicly funded education and indoctrination centers wholly run by the federal government.