Imagine a friend reads an article which uses scientific references to prove that vaccinations might be linked to autism.
He doesn't have a scientific background to critically examine the evidence, so he adopts the belief and finds others that feel the same. The belief becomes core to their group identity. The more he advocate in favour of this belief, the more heavily he is accepted as a member of the group. He feel united in a common cause. He's in the powerful numerical minority.
Let's call this group the believers.
Now an opposing group highlights evidence that disproves their beliefs. Let's call this group the non-believers.
To accept this evidence, the believers would have to reject the social group which gives them their own identity. That's not going to happen. Instead, the believers challenge the evidence. They look for any perceived error they can hide behind. They refuse to accept any evidence that changes their world view.
If they were to change their view, they would neither be welcomed into the opposition group and rejected from their own group. Worse still, any believer would have to endure the humiliation of backtracking on their often stated opinion.
Sure enough, the evidence becomes irrefutable. The believers still don't wish to lose their identity. They take a different approach. They claim a conspiracy! (it's impossible to prove there isn't a conspiracy).
It sounds maddening, but from an evolutionary psychology perspective, it's quite logical. Historically, we don't survive well when we're alone. We want to be in groups. To be in groups we need to show we're a reliable member. Sustaining group beliefs is how we do that.
3 years after President Obama released his birth certificate, 15% know for sure he was born outside the USA.
So why bother even trying to confront these groups?
Because 52% believed he was born outside the USA in 2010.
You can't change someone's views by presenting evidence. You can however do three things.
1) You can create personal doubt. When the issue dies down, someone might quietly change their mind.
2) You can present a different identity they can join. This identity isn't based on the typical believers/non-believers divide. Find a new paradigm to unite the group.
3) You can stop new members joining. Every new group needs a replenishment of members to survive. You can create that.
Always allow every member to express a relevant, legal, opinion. Never allow that opinion to pass unchallenged.