No, they're probably worried more about keeping their job and healthcare from day to day than about some dumbass policy at school that they know they can't change anyway since they have no time to go to the board meetings and don't want to get involved in crazy school board politics (yes, of course they exist). Some even say they don't want to rankle the neighbors with politics.
This is the reason that the person who did the final draft of the 1st Amendment, Fischer Ames, was a HUGE critic of democracy: People are busy. Really busy. they would not have time to help run the government! That is what is happening here.
This We're Smart and Everyone Else Is Stupid mentality you're fostering is part of the destruction of our country, a subtly vicious meritocracy, and it HAS to frickin stop if we want any progress. Parents are NOT dumb, they're over-frickin-worked and exhausted! They have little or no time to worry about rights. They just want their kids to get a good education (yes, I know the argument here...) They trust in the school system because it's the only thing available to them, and a host of other reasons.