A couple of years ago, the US's Center for Disease Control issued a leaflet which listed various "common knowledge" facts about the vaccine and labelled them as "True" or "False". Can't get much clearer than that, right?
When University of Michigan social psychologist Norbert Schwarz had volunteers read the CDC flier, however, he found that within 30 minutes, older people misremembered 28 percent of the false statements as true. Three days later, they remembered 40 percent of the myths as factual.
Younger people did better at first, but three days later they made as many errors as older people did after 30 minutes. Most troubling was that people of all ages now felt that the source of their false beliefs was the respected CDC.
These findings have been replicated in various other experiments: we just don't seem to attach negative markers to memories. You may have experienced this yourself: telling someone a story about how you e.g. went out and thought you'd left the iron on (but hadn't), and finding out later that they no longer trust you around home appliances because they remember the story but haven't filed it under "fiction". Or, for a more fun version, start introducing your friends to people they fancy with the words, "This is Geoff, who's never had chlamydia."*
The implications for this are fairly massive. For one, it goes some way to explaining why the HSE can't get a break. More seriously, it shows how easy it is to spread falsehoods even when you're trying to fight them. The more you talk about, for example, how MMR doesn't cause autism, and there are no good studies that link MMR to autism, and that studies that do link MMR to autism are flawed then the more you're linking MMR to autism in people's minds. Denying false allegations is such a natural response as to be almost reflex, but if that's all you do then you're just going cement the falsehood in some people's minds.
Instead, if you've got a point to make, make that point. Don't say "MMR doesn't cause autism," say, "MMR is safe". Instead of "Immigrants don't steal your job" try "Immigration makes us better off". As LBJ pointed out, there's no weaker position to be in than denying something that's not true.
*NB, this works better if your friend is actually called Geoff.