The trouble with IQ is that it doesn't really mean anything. IQ is supposed to be an absolute measure of intelligence, one that is the same from the day you are born to the day you die and that depends on nothing other than your brain. Unfortunately, it isn't. All an IQ test measures is your ability to take IQ tests, and it is very easy to practice and improve. This makes the whole thing pretty pointless, since you could have an average IQ one day, take a course in maths and logic and end up 10 points higher a couple of weeks later.
There is also the problem that there isn't really any good definition of what intelligence actually is. Is someone who can do long division in their head more intelligent than someone who can write a piano concerto? What if you can do both, but have trouble tying your laces? The sort of questions IQ tests ask tend to focus on maths, logic and spatial awareness, which are certainly useful things to be good at, but are far from the only things that matter in life. If you want to be a scientist, a high IQ is generally a good thing. If you want to be a social worker, how is it relevant if you can work out which coloured square comes next in a sequence?
Finally, a problem that I have myself is that if you find those sort of questions easy, there are usually several answers possible. This means that instead of being a question that you can either get right or wrong, it becomes simply a game of guessing, or knowing from experience, which answer the questioner wants you to give. No doubt this is also a useful skill to have, but is not supposed to be anything to do with IQ tests.
Basically, all that waffling is trying to say that IQ is essentially meaningless. If you're going to be doing a lot of the sort of thing IQ tests test, then they're a decent test of your ability. If you're not, they're completely pointless. In addition, most of the tests you see around aren't just trying to test something that's poorly defined, they don't even test it properly. If a free online test tells you you have a certain IQ, don't believe a word of it. Professional tests tend to at least be consistent with each other, but as I say above, what they actually mean is not much other than your ability to take the tests.
As for why people believe things, I suspect there may actually be some correlation with IQ. IQ tests look at logic and spatial awareness, which are exactly the skills needed to avoid many of the traps believers fall into. However, note the important word "skills". You can learn logic. You can improve spatial awareness. There is certainly some genetic component as well, but IQ is nowhere near as fixed as some people would like to believe. Similarly, just because some people believe weird things now does not mean that they always will, as many posters here can demonstrate.