This view is very interesting, and you are compassionate. Ime, these people share a strange mix of traits; under-educated, ignorant, confident and arrogant. They seek an easy path to form a pseudo self-esteem; our small secret club of enlightened members who put in very little effort know more than all the mainstream educated sheep with their thousands of hours of rigorous study. Even though it's the latter camp's math and theories that have given the world all of it's accomplishments and values that the former camp uses daily. WTF? I view this phenomena as laziness more than mental illness (although now you've got me thinking that laziness IS a form of mental illness). You are absolutely right that using our tools of logic, reason and evidence is usually useless. As Sam Harris states,
“If someone doesn't value evidence, what evidence are you going to provide to prove that they should value it? If someone doesn’t value logic, what logical argument could you provide to show the importance of logic?” I don't participate in an oppositional stance against these folks as much as I used to, especially when learned others are already fighting the good fight. Although their (pseudo) self esteem seems tied to their erroneous beliefs, I'd argue that it's really their self esteem they are protecting rather than their actual beliefs, which are obviously useless. It's not us they are attempting to fool, but themselves. I don't mind these people having these ideas, it's the arrogant, blustery certainty with little to no mettle behind it that bothers me. If they kept it to themselves I'd have no problem, but when they attempt to spread that shit in public forums, it bothers me. Mainly because it is possible to spread that diseased thinking to laymen who don't know any better.
Public ridicule seems to be a great tool for preventing the spread of really bad ideas, to the benefit of everyone. For example, there are people who believe Elvis is still alive, but one rarely hears this belief stated publicly. Why? Because one pays an immediate price for such a declaration. Imagine this belief stated at a job interview, or a first date, or at a party. The person stating this tripe would be openly laughed at, with no real concern of hurting the person's feelings or disrupting their mental state. While this would probably have little chance of effecting the erroneous belief, it keeps it deep in the shadows, away from infecting others. It is fascinating that there is a strong correlation between incompetence and arrogant certainty. It is widely known as the Dunning-Kruger effect. Check it out -