You keep them out of public schools to reduce the chance of them exposing other people as much as possible. Their co-religionists aren't likely to press charges, and many of these extreme religious groups don't want their kids in mainstream schools anyway.

In other words, you can use government-funded schools or you can refuse vaccination (and pay for your kids to attend a private school that allows unvaccinated students, or homeschool them and do the work yourself). You can't have both. That's how school vaccine mandates are supposed to work in the first place. We've just gotten way too lax about upholding and enforcing them.