I don't understand… are you asking me to make their arguments? :-)
I suppose the top indoctrination would be the teaching of evolution. Next, the absence of "equal time" for teaching ID. And, of course, not allowing public prayer (and forcing non-believers to hear it) is a key complaint. There's a lot more, including the "failure" to teach (in the South, especially) the "positive"aspects of states that practiced slavery.