I'd have thought it was America, what with all the crazy puritan descendants there.
Antivaxxers are far more likely to be New Age hippy-types than anything else. There's a few Christian denominations that are anti-medicine (and thus anti-vax) but they're a minority.
Really? Huh. Wonder why I was associating it with Bible belters, then.
As I recall, they were the ones who really got it started. I can't speak as to whether the conspiracy theorist/alt-med hippies outnumber them, but if nothing else the religious/deeply-conservative branch of the movement is still the most vocal. The main push from them comes from bogus medical studies claiming vaccines "cause autism" or that they're wildly unsafe for illogical reasons (e.g. "it's possible to make them incorrectly, therefore we should abandon the practice entirely.") There's definitely a weird amount of overlap; "alternative medicine", especially anti-vaxxing and homeopathy, finds adherents both among magic-crystal chakra wizard types and faith healing "cancer is also God's plan" sorts.
There's a certain amount of political alarmism involved, as well; a common thread is "vaccines deny people individual liberty", because apparently potentially killing or maiming both yourself and others is less important than not getting half-dead microbes injected into your arm. This was actually the main thrust of an anti-vaxxer I debated on the internet once, who believed that making people get vaccines will cause the United States to become a totalitarian dictatorship.
Anti-vaxxers have been around since vaccination was invented. There was much opposition to the smallpox vaccine, mostly because a lot of scientists thought that the whole thing was bunk, and smallpox was caused by bad air. There was a small religious opposition, but the main source of opponents were objecting on scientific ground.
In the 1970s, there was considerable opposition to the Diphtheria, Tetanus, and Pertussis (DTP) vaccine. This appears to be solely based on claims that it caused brain damage. There was a massive drop of DTP vaccination (and resultant outbreaks) in the UK, but the panic never set in in the US.
The modern anti-vax movement only really got started when the maker of a rival MMR vaccine started spewing out lies to discredit the one in common use. As with the DTP vaccine, the whole mess started in the UK before spreading to the US. Unlike with the DTP vaccine, this time around stupid celebrities gave this nut a voice, and it fireballed from there.