In my experience, anti-vaxxers lean both left and right, often for different reasons.
I think it varies by region. Where I live, the anti-vaxxers tend to be left wing extremists. It's the same people who believe all scientists are corrupt and Monsanto is the devil and GMOs will destroy the world, yet do believe the scientific consensus that climate change is real because science says so. They think Big Pharma is out to get them, and that cancer patients should eat avocados lemon water instead of undergoing chemo. They profess that the paleo diet is how everyone should eat, and think that eating gluten will killing them. They are rabidly anti-corporation, but spend most of their money at multi-billion dollar publicly traded Whole Foods, and those that don't have a lot of money malnourish their children because it's better to eat "clean" than eat enough.
They are part of a religion. That religion is composed of the faith that anything that seems unnatural is evil and is trying to kill them, and everything is part of a conspiracy to force unnaturalness on them.