Most states allow for some form of exemption from that rule on religious or personal belief grounds. I think California, New York, and Mississippi are the only that don't.
It's not moot though...I love vaccines and 100% support them, but I understand why people fear them. To me it is absolutely unacceptable if we as a society think it's OK for someone to be coerced into allowing a strange substance injected into their body. Now, if you can convince them to willingly do so (because the body of evidence supporting vaccine safety is overwhelming) then that's great! But if they're say, of a religious denomination that holds the body is a temple of God and using medicine or technology to prolong life is a sinful affront to his Will (people like that are out there), do we have a right to override their 1st Amendment rights just because we believe differently? I don't believe so.