Conservatives want to pass their values and culture and mythology on to their kids. But, for many of them, public schools are an obstacle to that. The key problem in the conservative mind with public schools is that the melting pot has given way to a multiculturalism that creates a climate of fear regarding ones own culture - exactly the opposite of what people want.
This isn't just public schools, and it isn't about religion, its everything conservative these days - lower taxes are just a form of saying, "I disagree with the public direction, so I want no public at all." They are allowed to say that, and when the liberals call them selfish for it, the end result will be a hastening to this trend of withdrawal. Why participate in something that is detrimental to you, and you don't believe is good for the public overall?
The ironic thing is that, even though liberals talk up a good game about the commons, you'll find they are withdrawing from the public as well. Of course, its long been known that rich people send their kids to private schools regardless of their political stripes, but you'll see it in their spheres.