With a school-vouchering system it is likely that some more secular private schools would pop up to take a piece of the pie. Introducing this system would put these schools into a position of competing for students based ont he academic quality of their education, this is a good thing for kids. On the other hand, its also posible that some really wacky parents will be able to set up schools with the sole intention of indoctrinating their kids into their way of life.
For example, we dont currently have an actual neo-nazi elementary school, largely because the people who would enjoy such a thing can not afford to support one. With a vouchering system such a school could exist with state funding in the form of vouchers. I dont know how important that is, but it rubs me the wrong way that my tax dollars could be spent to such an end. The current system of private schools ensures that they have to make some kind of sense to people because they are spending their own money on them.
The obvious solution to this is to, of course, set up some rules about what schools can accept a voucher, but really, that is the part that worries me the most. The government will almost certaionly exert even more pressure onto schools under a vouchering system. Meaning, that if a school is allowed to accept vouchers they would have to conform to a set of federal guidelinges, making the private schools very similar to public schools and defeating the whole purpose of having them in the first place. Logically a school would be able to simply deny vouchers, but in a system where vouchers are the norm it might become difficult for a school to survive without them. Furthermore, when people start paying private school tuition with someone elses money, they stop paying as much attention to how that school operates. If a school suddenly has 10 times the applicants than they have seats, it becomes less important for them to actually please their current parents.
Really, i see this whole vouchering idea as a solution in search for a problem. The problem is that public schools kinda such. Well, maybe we should fix them, except that a big part of the problem with public schools is the very nature of them being public. Private schools exist as an alternative for people who want their children exposed to better education and their own values. Vouchering will do nothing to fix public schools, in fact it can quite possibly make them worse, and I dont think it will improve the quality of private schools eaither.