Anti-vaxxers, as some call them, are impervious to facts the same way extremely religious people are impervious to facts which conflict their beliefs. Their belief is founded on faith in something other than standard science. In some ways, it is a quasi-Communist worldview, imagining conspiratorial cabals involving drug companies, the government, and physicians who are either shills or dupes.
The Internet's vaunted "democratization of knowledge" bears much of the blame.
From this article:
The Vaccine article contains a number of important insights. First, the anti-vaccination cohort likes to move the goal posts: As scientists debunked the link between autism and mercury (once present in some childhood inoculations but now found mainly in certain flu vaccines), most activists dropped their mercury theory and point instead to aluminum or said that kids received “too many too soon.” "Web 2.0 facilitated the debate of these new theories in public forums before their merits could be examined scientifically; when they were studied, the theories were not supported,” notes the Vaccine article.
Second, it isn't clear whether scientists can "discredit" the movement's false claims at all: Its members are skeptical of what scientists have to say—not least because they suspect hidden connections between academia and pharmaceutical companies that manufacture the vaccines. (This, in itself, is ironic: In 2006 the British investigative reporter Brian Deer revealed that Andrew Wakefield, the British scientist who famously “showed” the connection between vaccination and autism in a now-retracted 1998 article in the Lancet, was himself handsomely compensated by trial lawyers who were readying to sue the vaccine manufacturers.)
In other words, mere exposure to the current state of the scientific consensus will not sway hard-core opponents of vaccination. They are too vested in upholding their contrarian theories; some have consulting and speaking gigs to lose while others simply enjoy a sense of belonging to a community, no matter how kooky.