There have been many studies into what makes people hold views that seem, to most of society, totally counter-intuitive. An American study (by Leon Festinger) in 1957 was the first to use the term 'cognitive dissonance'. It basically refers to someone simultaneously holding views that are contradictory. It was originally identified in cult situations, where intelligent, caring people made and justified decisions that seemed to fly in the face of their own internal logic. Subsequent research has shown that simply telling someone their view is factually incorrect or contradicts their own belief system simply doesn't work. This understanding is applied every day by professionals. When experts work with young people drawn into extremism or gang culture, they don't simply stand in front of them and yell 'you're an idiot and your ideas don't make sense.' Actually, this has been shown to entrench views still further.
The only way to change someone's thoughts and feelings is to understand them and try to see the world through their eyes. Kindness, understanding and empathy are generally considered the best approach, even when the instinct of the youth worker is to say 'can't you see they're using you' and the Priest or Imam just feels like shouting 'He never said that!'
Generally, people adopt viewpoints and lifestyles not to stand apart, but to belong. If you are on the outside, it's often difficult to see the appeal, but every viewpoint and way of living tends to have its own community. The people who join those communities don't feel like they are sufficiently cared for or belong in the 'mainstream'.
All over this is true of people on the fringe of society, but it is also true of all of us. At the moment, political and social discourse is often polarised and many of us are faced with people we care about adopting views we abhor (often understandably). If we truly care about those who hold such opinions, I suspect the answer is not to rant at them or present them with our 'truth'. This can make us feel better, and maybe even more worthy. To listen, understand and include them, so that they feel they have a stake in our own world is much harder (and often counter-intuitive.)
I'm not writing this from some 'holier than thou viewpoint'. I am as capable of holding a strong opinion as the next person, probably more so (as friends, family and colleagues will attest!) The thing is, I don't like the way the world feels at the moment and I meet very few people who do. I'm pretty sure open conflict won't heal our wounds. I can't think of a single instance of someone turning around after a verbal onslaught and saying 'Now I see your point. I was stupid to think that. I am, as you point out, a right knob!'
I know as a counsellor I'm bound to say this, but we could probably all benefit from a little less judgement and a little more empathy. It might just prove to be the secret weapon we've not yet employed. And what better time to start?