Right now, religions - at least, some
religions - get extra legal benefits that the non-religious don't. Government employees get extra time off for relgious holidays; the non-religious get nothing. Religion is family of metaphysical worldviews, and non-religious philosophies are another branch. Why do certain philosophies get extra privileges?
If a rule really is a good idea, then it should apply to everyone. If we can get by with some people not complying, then it doesn't need to be mandatory. Religion has nothing to do with it.
In terms of vaccines, we just need to arrange for consequences. Your kids not vaccinated, and can't demonstrate a medical reason why not? Fine. No public school for them, sorry. Quite probably other benefits are now off-limits, too.