I think that many people who believe things like this share the following beliefs:
1. Anecdotal information, especially when it's personal, is more convincing than statistical analyses. For example, there are a few strange artifacts that some creationists believe are fatal to the theory of evolution; similarly, there are some emotional case-stories about kids with autism that can sway people to forgo shots.
Why is this misleading? Because human brains are trained to see patterns where there is none, anecdotal information can be misleading. Broad statistical methods are designed explicitly to address these sorts of issues.
2. It is possible that powerful groups in society are secretly operating vast conspiracies against the people. Creationists believe that biologists are actively collaborating to prevent their false believe in evolution from being exposed; anti-vaccine advocates believe that the entire medical (or, perhaps, pharmaceutical) industry is conspiring against them.
Why is this misleading? Although our government is not exactly "open source," it is impossible to coordinate conspiracies as vast as the ones required to support some of these theories. In particular, science is very competitive, and scientists are skeptical of other scientists' work. I can't even imagine how someone would get all of us to agree to mislead about data. Also, bureaucracies are incompetent.
3. Sharing radical ideas provides a deep connection with people, even over the internet. I am sometimes struck by the reasonably cohesive nature of these sets of people. The best example of this is moderated internet forums or blogs where large sets of people, all in agreement with each other, can discuss the issues without dissent. If you are a creationist, you might feel an instant connection when, say, you sit near another creationist on an airplane. By contrast, it is entirely unremarkable to meet someone else who accepts the evolutionary worldview.
Why is this misleading? This is a trickier one, because it has more to do with human society than any particular worldview. However, I can speak from personal experience. Some people think that people's political views are a good predictor of whether or not they will make good friends; I have found this not to be the case. Hanging out with people who disagree with you can be much more interesting, and I think personalities cannot be pigeonholed like that.
The really surprising thing, to me, is that I understand why these ways of viewing the world are appealing. As a parent, I rely to a great extent on anecdotal information about how to handle certain situations with the boys. I think the current administration is operating, for the most part, under a cloud of secrecy. And I like radical ideas, and feel bonded to others who can think "outside the box." But together, these things are a potent cocktail for misunderstanding.
To me, this is relevant to my teaching. Perhaps science classes can help students reconcile their framework for the world with scientific information, so that they aren't taken advantage of by these sorts of, to me, counterproductive movements. There are strong arguments against all three of these viewpoints when it comes to complex issues; anecdotal information is deceptive, bureaucratic organizations are too incompetent to really succeed in fooling everyone, and radical ideas don't really lead to lasting relationships. Perhaps we should think about how to get this sort of information across.
One reason why I wanted to post this is that I think the common way of interpreting creationists as "nutcases" or "religious fanatics" is not really a proper explanation (the cartoon here illustrates this way of thinking). In fact, the belief that people who disagree with you are less intelligent and morally inferior in some way is a common thread that is lurking behind many issues in society today - in fact, perhaps both Bush and Bin Laden share that way of thinking. But that seems like another post. Here, my goal is to point out that there are real reasons why people hold the beliefs that they do. If you want to really affect these people - or even coexist with them - then you have to get to the core of the issue.