The best answer to your concerns is there is a private school for those also?
If not make one!!
Of course.... that may no longer apply when they are receiving money from the government in the form of a voucher! I can easily see a situation similar to what occurring with student loans and colleges happening to private schools. After letting all the private schools get used to all the extra income a flood of parents with vouchers will supply... the government will simple come in later with demand X. With the threat that if demand X isn't complied with vouchers will no longer be allowed to be used at their school.
This will then be used to impose every left leaning crack job idea imaginable onto the private schools.