From my personal experience they've always tended to be further right, since often the anti-vaccine fear comes as a result of government mistrust as well as not trusting scientists. Very similar to the people against climate change in my opinion.
Though it's true that the anti-GMO and even anti-Nuclear sentiments I see accross the spectrum but those differ a bit from conspiracy theories in that it stems from junk science, rather than a belief in a hidden government or group wanting to personally change you.
My experience couldn’t have been further from yours. Most of the anti-vaxxers I encountered both irl and online were of the kind that is all about natural remedies and distrusting of GMOs and such (as opposed to those distrusting of government and believing in conspiracies; that kind i mostly encountered online only).
Just google for outbreaks in the US that are linked to anti-vaxxing and take a note of their locations. Most will start in heavily left-leaning areas. To clarify my point, I personally believe that anti-vaxxing is about evenly distributed between left and right wing, just for different reasons.
Though it's true that the anti-GMO and even anti-Nuclear sentiments I see accross the spectrum but those differ a bit from conspiracy theories in that it stems from junk science, rather than a belief in a hidden government or group wanting to personally change you.