Yes a parent should be able to choose which schools-the same way they choose any other product in a capitalist society: via the free market. the best products will survive, the worst, schools like public school caliber, will not.
That's where freedom 'OF' religion as well as freedom 'FROM' religion comes in. It's pure choice! They should be able to say no to liberal studies on that basis. Liberalism is the opposite of Christianity. A patriot is the opposite of a socialist. None of those things I posted earlier would be taught unless the school chooses to do so, but the parents can say "No thank you. I'll go somewhere else."