The first amendment protects them here.

That depends on the court, and on how broadly the relevant rule is written. It's a hell of a claim to say that my religion must exempt me from laws that apply to others, and that's exactly the sort of claim being advanced when we say that our religion requires us to not do [things that our religion says nothing about].

A relevant precedent, in Jacobson v. Massachusetts, reached in 1905 regarding the constitutionality of compulsory vaccination law, held that individual liberty is not absolute and that the public interest can justify narrowly subjecting it to the authority of the state. (note that this ruling was narrowly about public health authority and its enforceability, and the stakes of the dispute were that if Jacobson didn't want to be vaccinated, he would be made to pay a fine and nowhere was child custody ever questioned)

The Court held that "in every well ordered society charged with the duty of conserving the safety of its members the rights of the individual in respect of his liberty may at times, under the pressure of great dangers, be subjected to such restraint, to be enforced by reasonable regulations, as the safety of the general public may demand" and that "[r]eal liberty for all could not exist under the operation of a principle which recognizes the right of each individual person to use his own [liberty], whether in respect of his person or his property, regardless of the injury that may be done to others."

Personally I agree there shouldn't be religious exemptions on vaccines, that the only cases that justify non-vaccinated kids attending schools would be medical justifications, not religious ones. Allowing non-medical people to carve unscientific loopholes in best public health praxis because they feel like Jesus or Cthulu (neither of whom said to not get vaccines) wouldn't want that basically means, if you extend that reasoning to its logical end, that when I say I have a religion and I tell you it means that law cannot apply to me or else it violates 1A, that no law can be consistently made to apply to anyone. ...and when it can't be made to apply to everyone equally, expect it to be applied, forcefully, to people of the wrong faith, or of the wrong race, or of the wrong caste.

A lot of these anti-vaxxers would be fine with not educating their kids.

OTOH, a bunch of them would just want to educate them at some sort of vaccine-free school or something, which they would presume would get government money. As long as they don't get money....