I've heard it said that reactionary, private, and allegedly Christian schools that use the same basic curriculum as public schools but with a Bible class added on remain basically un-Christian schools. This seemed right to me, though I wasn't sure why. This paragraph from Littlejohn and Evans explains it.
Secularization is not the removal of the sacred from society. It is, rather, the compartmentalization of the sacred within society such that the sacred is no longer allowed to speak in a normative way to society. This, of course, describes precisely what has happened in the United States. We are told that it's fine for us to practice our faith on our own. But we are also told not to think that our faith is in any sense normative for the anyone else, let alone the rest of society. This is secularization. The sacred is placed in its box separate from everything else, and there it is to stay.