Further, it's not simply a matter of parents choosing a private school but of private schools choosing students. And the school's choice always wins. If a private school doesn't want your child, whether for academic, disciplinary, religious, or financial reasons, there's nothing you can do. And this needs to take place in the broader context of fighting for a better education for all kids. The possibility for democratic discussion of what is best for all our children would virtually disappear under a voucher system.
Many religious schools have a strong track record on educating kids.
The core issue is that individuals would be paying tax money to support schools with religious values that might be antagonistic to their own religious values. Religion is a profoundly private matter and should remain that way. Wouldn't vouchers allow lower-income families to send their kids to private schools and get a better education. In the long run, abandoning public education will only increase inequalities in education. And they would force private schools to accept all students who apply, based on a lottery system.