It's been true for some time that conservatives are far more likely that liberals to hold a number of false beliefs about the world, some of which were always political (e.g. Saddam had weapons of mass destruction, evolution is a myth) and some which became more political over time, particularly the belief that the planet is not warming and its subsidiary beliefs, which include the idea that there is a great deal of disagreement among climate scientists as to whether warming is occurring. Sometimes when this is brought up, someone will mention that liberals believe some demonstrably false things too, like the idea that childhood vaccines cause autism.
The trouble is, there has never been anything other than anecdotal evidence for this contention. Yes, there may be a parent at your kid's organic vegan locally sourced small-batch co-op nursery school who thinks it's true, and dangerous lunatic Jenny McCarthy, the nation's most prominent propagator of this theory, is a Hollywood celebrity and many Hollywood celebrities are liberals, but that doesn't mean that liberals in general are more likely to believe in the fictional vaccine-autism link.
So here is some empirical data, from Dan Kahan of Yale Law School and the Cultural Cognition Project. Kahan did a study that included a survey and some experiments testing both what people believe about the topic and how they react to different kinds of information about it. And it turns out that not only do very few people believe that childhood vaccines pose a danger, liberals are no more likely to believe that than conservatives; in fact, they're slightly less likely to believe it. Here's the key graph, which shows how much risk people of different ideologies associate with a variety of things like legalizing marijuana, gun ownership, and global warming. The black line is vaccines:
So there you have it. The perhaps more troubling finding comes from Kahan's experiments, where subjects read an op-ed making one of a number of arguments for vaccinating, and were then asked their feelings about vaccines. One of the op-eds, which was framed with contempt for "anti-science" people who don't believe in evolution and global warming and also believe in an imaginary link between vaccines and autism—precisely the kind of op-ed a snooty liberal might write!—actually produced polarization, pushing some people into the anti-vaccine camp. He explains:
Whereas subjects in the control were not meaningfully divided over vaccination risks and benefits, those in the "Anti-science" condition showed signs of polarization. Exposure to the "Anti-science" op-ed significantly weakened the positive affective orientation of subjects with a cultural style that features concern over social-deviancy risks—including legalization of drugs and teaching of sex education—and that is associated with religiosity and disbelief in evolution. As a result, a meaningful gap emerged between subjects with this cultural risk predisposition and subjects with alternative predisposition, one that is associated with a secular outlook and that features low concern for social deviancy risks and greater concern over climate change and gun control.
To translate, the op-ed heaping ridicule on the anti-vaccine advocates essentially sent a tribal signal to (some, not all) conservatives, saying that the anti-vaxers are your kind of people, or at least, the people you hate also hate anti-vaxers. They responded by moving over to the anti-vaccine position. So liberals, take note: if you want to convince as many people as possible, when you're talking about this you should consider the opposition to vaccines a unique, non-ideological misconception, which it is.