Talking to anti-vaxxers is basically signing a deal that you agree to be repeatedly told lies. But how do you state your case when you're coming up against real whoppers?
In the anti-vax movement, anecdotes are everything. When there is no peer reviewed research to support the point, they tell you've they've seen it with their own eyes. Of course, anecdotes are not research, but at least with most groups, you can trust that those people really believe what they're saying. With anti-vaxxers? All bets are off.