lesschumras, AFAIK school choice doesn’t mean private/religious schools are publicly funded the same way public schools are. I’m no expert, but I believe the idea of vouchers is that part of the tax money that’s allocated for each student follows the student to the school of the parents’ choice, whether it’s public or not. Please correct me if I’m wrong.
Even without vouchers, private schools have to meet certain standards. Otherwise, they parents could get in trouble for not sending their kids to (a real) school.