I would be curious not just where the political line is drawn, but how it shakes out specifically among the donor class within each side of said political line. Anti-vaxxers definitely lean left. By a large margin, it's not even close. Especially if they are wealthy. And they all shop at Whole Foods, the number one peddler of $10 bananas and other magic potions. Now owned by the same guy that owns the Washington Post. The math is easy. Talk about white privilege. What a pretentious store that is. A visit to Whole Foods is like a visit to The Capitol from the Hunger Games. I do love their selection of kimchi though. But I'm privileged, so there, suck it. If I ever walked in that store wearing a Trump shirt I doubt I'd make it out alive.

Another problem too is that "anti-vaxxers" comprise a wide spectrum. Conservatives generally only sympathize with the movement in that they are averse to compulsive government programs. So a parent doesn't want to vax their child? Who cares. If your child is vaxxed, what are you so afraid of? I vax my kids, but I'm not sold on forcing anyone to vax theirs. I also am not sold on all vaccines. Like chicken pox. I've opted my kids out of that one. I think it's stupid and unnecessary. We have kind of a sissy pill popping culture that is averse to pain. Chicken Pox is a right of passage, in my opinion.
These surveys are always silly because they never take into account the complexity of an issue and the variance of opinion. Like RI points out, the left vs. right will push back on the vaccines for different reasons. But what are those reasons, and what level of push back results from them?
The ones on the left literally believe in this weird Big Pharma conspiracy where twisted docs in lab coats, white men nodoubt, are intentionally harming children for personal profit. They know it's doing damage and just don't care. The ones on the right don't believe anything like that is going on, they just don't like being told what to do, by force, and generally are suspicious of anything managed by the one true bureaucracy, even the US federal govt, in an eye rolley sort of way. The government approach is to administer any vaccine that's available, when in truth only a fraction of them really matter. But when those people push back, even just a little, they get branded as "anti vaxxers" and tossed in the same basket as the others. The people who are fiercely anti-vax, truly opposed, talking about it leading to autism and such claims, always, always, always, on the left.
I submit, one of the most anti-science groups in the country - Liberal Mormon Women. You want to see a group of anti-vaxxers, find yourself a feminist Mormon moms discussion group on Facebook.