I like to think of myself as a rational person, but I have had my moments. When I was 8 or 9 years old, I fervently believed that there was a bear living under my back porch who would eat me if I went into the backyard at night. I have no idea where this belief came from. There was no evidence to support it, and I never told anyone else about it because I knew they would think I was just being silly. I even felt silly believing it, but the fear was still there. Regardless of what I could observe for myself in comfortable daylight, I still felt completely certain that at night there was a bear, and he wanted to eat me. Eventually, my Dad unwittingly forced me to face this irrationality by making me go into the backyard one night to put away my bicycle. Amazingly I survived, and the fear gradually diminished.
A belief is not the same thing as a thought or a feeling. A belief has conviction. It is something that we somehow know to be true in a personal way, and it has the power to make us act irrationally. If I truly believed that doctors were murdering babies in abortion clinics, then I would be doing everything I could to stop it from happening. As a scientist I know that is simply not the case, but knowing something is not at all the same thing as believing something. If someone had told me as a child that there was no bear under my back porch, you'd think I would have been relieved. 'Oh, how wonderful! Now I can stop living in fear! At last, I am free to play on the porch at night!' I can tell you with reasonable certainty however, that is not what would have happened. It would have hurt my feelings. I would have felt the need to defend my bear's very existence to you, because if he wasn't real then I was acting very silly for no reason. In fact, if my Dad had not motivated me to face my bear I may have continued to believe in it until I was far past the age where such things are amusing instead of worrisome and inappropriate.
This is not a perfect analogy. The existence of a bear is much easier to disprove then, say, that of a deity. What I am really trying to accomplish with my little anecdote is to encourage patience and understanding. When you encounter someone who believes that, say, the Earth is only 6000 years old, citing evidence and describing alternate theories is unlikely to accomplish much. If it is possible instead to somehow nudge said individual into asking questions on their own (perhaps through recommended reading or simply by example), your chances of having an impact improve. Yes, it will be harder. You may even have to accept that they are not ready to deal with the repercussions of re-evaluating their beliefs and let it be. Also difficult.
I would also encourage individuals to take a quick look at what they believe. Maybe even a long one. As an atheist I strive to question everything and prioritize rationality, but even so I still find myself still caught up in something that has no rational basis. For years I wouldn't eat mushrooms. Why? Because they were fungus. Six months ago I realized that portabellos were delicious and have never looked back.
Obviously I am making light of what can potentially be an extremely troubling issue. Abortion doctors and clinics are constantly subjected to violent attacks. Human beings strap bombs to themselves and detonate them in public areas. Parents pray for their children instead of taking them to see a doctor, even if the disease is life-threatening. These acts are not rational. In many cases they fly in the face of scientific facts, and those that commit them generally cannot be reasoned with. So what can the rational masses do about this, aside from cringe and occasionally hide under the covers? The only real answer I see is education. The open dissemination of information. The internet has already had a huge impact (This is a great video on the subject if you haven't seen it: http://www.youtube.com/user/Thunderf00t#p/a/u/1/0Rqw4krMOug
), and will continue to do so. I may be a bit biased, but I like to think that scientific thinking can save the world. I do my best to spread the word, so to speak, by volunteering at science fairs and school science programs. Science is awesome and I want to help people understand it. http://www.xkcd.com/154/