This post from PZ Myers raises a very important point about decentralisation and local accountability. What if the quacks get control? Families and schools are always a problem with regard to liberty - no-one has the right to experiment on the public without their consent, but youth is the one experiment that is performed on everyone.
It may be your right to believe that heliocentrism is an atheistic doctrine that must be suppressed, but it's surely a grave infringement of the liberty of others to enforce it on their kids. Not to mention an infringement of the children's liberty. The glib answer is that you can always send them somewhere else, but this instantly crashes into all the problems of "choice" as a solution for schools (inequality, oversubscribed schools, self-fulfilling signals, lack of real choice in many places), not to mention that it implicitly accepts that the people left behind will just suffer.
Robert Waldmann remarks that there is no evidence that any society has ever put too much money into education. I think he's right. But this is rather what I was getting at in this post. Education is an investment that cannot be readily replaced if it goes wrong - in the example it's much more like the hole in the ground that you can't replace in 50 years than the Ethernet switch, which you can swap out in half an hour. Hence, it's not enough to say that if the creationists (or paedophiles, fascists, jihadis etc) get a school, it will eventually fail. By then the damage is done, it cannot easily be put right, and it bears most heavily on those least able to put it right.