Being perceived as "smart" is a privilege, and it's just as irrelevant to being anti-vaxx as all the other privileges are (in fact, many of those who someone like you might not perceive as "smart" - disabled people, and specifically autistic people, are the open target of anti-vaxx propaganda that frames us as an undesirable thing to be, for, amongst other things, not being "smart"). So I'll say it again - tons of well educated and otherwise privileged people are anti-vaxxers, and pretending otherwise isn't just classist and ableist, it's also just plain wrong and counterproductive.