I mostly associate anti-vaxxers with far-left Californian soccer moms, not anyone on the right.
Although I think far-left Californian soccer moms are responsible for the majority of helicopter parenting, anti-vaxxers seem to often be the people who homeschool and think that public schools are trying to convert their students to Islam. Nonetheless, I think that the anti-vaxxer movement is a consequence of decades of "think of the children" movements that were often pushed by doctors, schools, scientists, etc.