As a Libertarian I say at the minimum allow vouchers so that students may attend any accredited school they wish, including religious schools.
Having said that, I don't think there would be a hugh shift to Biblically strict schools. There is a common belief held by the very religious that somehow the state is imposing an atheistic view against the will of the majority. In fact the majority pretty much likes the schools as they are.
Of course there are many that are priced out of religious education, and those people would switch given vouchers. But the majority of parents would try to send their kids to the best academic schools, not the most religious schools.
One only need look at the situation for college education where religious and secular institutions are on otherwise equal financial footing. Secular institutions are quite well represented.