Answer: the states with more atheists per capita - because in America they share a political and cultural demographic that is inherently anti-science. But I have good news for those anti-science people; an actual religious person has filed for a philosophical exemption, which means they can now claim anti-vaccination beliefs are 'bipartisan', just like anti-science beliefs about GMOs are bipartisan if 2 members of Congress out of 55 calling for warming labels are Republican.
Dina Check, a Catholic, says she wants a religious exemption from vaccines for her child. Now, I have read whole books on Vatican II and while it has completely messed up the modern church, nowhere in there does it or a Pope say vaccines are bad. Sure, they are against condoms (correctly - those are awful) and the Pill (they should reconsider that, it is awesome) but not vaccines. Of course, this is a New York City Catholic. Like Secretary of State John Kerry, lots of northeastern Catholics are the a la carte kind - they pick and choose what they like from a menu, just like they do with science, that is why John Kerry can support abortions and then go to communion without any of that famous Catholic guilt. And also why Dina Check can hurt her kid and feel like she has a moral standing, even though the actual Roman Catholic church disagrees.
As Tracie Egan Morrissey at Jezebel writes, this seems to be sort of a ruse; Check had tried to get an exemption on medical grounds and was denied. Gastrointestinal problems and vaccines? Debunked a decade ago. You can see what kind of crackpot we are dealing with already.
Of course, the libertarian mentality says government should not be forcing kids to have vaccines and this is forcing; the child cannot go to school financed by the public without the vaccines. But she wouldn't be allowed in school wearing a Nazi shirt or carrying a gun either. There are limits to personal freedoms, even under the Constitution. You can't yell 'fire!' in a crowded theater, an admittedly government-heavy Supreme Court found (Oliver Wendell Holmes is the fawned-over progressive Justice who also believed eugenics was completely okay) and if you bring leprosy into the US today, you will find your Constitutional rights rather limited.
Maybe, if she really thinks vaccines are "invasive and unnatural substances", she can move to California and join her fellow believers - a school here has almost no children vaccinated, a startlingly low 23 percent (Science Left Behind, pp. 110-113). The Waldorf School of the Peninsula in California's San Francisco Bay Area also has almost as few religious people as it has Republicans, but their anti-science beliefs should make up for it.