Religion is not such a mysterious phenomenon -- it is deeply embedded in the world's cultures, from that long span of millennia when we just didn't have any better explanations. We grow up believing what our parents teach us, and religious belief is often the most powerfully indoctrinated kind of belief. Religion also gets a boost because it meets certain psychological and perhaps social needs of some people.
But the other forms of anti-rationality that seem to be rampant today are harder to explain. Sure, in some cases there are well-moneyed interests that expend substantial resources promoting nonsense -- from homeopathy to climate change denialism and the anti-vaccine movement that wants to sell you bogus "immune system boosters" and treatments for autism. On the other hand, the financial interest behind AIDS denialism doesn't amount to much more than Mathias Rust and his vitamin pills.
Even so, financial backing doesn't really explain the attraction for many otherwise smart and sane people who, after all, have the opportunity to learn the science and make up their own minds, but seem to find something liberating or empowering about slurping up the Kool Aid. The fact is a rift has developed between the institution of science and a large chunk of the public. Scientists practice in exclusionary settings, speak their own languages, and generally think it is demeaning or compromising to try to communicate with lay people. And indeed, that can be a good way to damage your chances for tenure. Many a scholar has been driven into the wilderness for writing popular books (viz. Paul Starr).
In the area of health and medicine where I happen to know something, anti-science movements kill people flat out. For example -- and it's only an example -- Peter Duesberg, the father of AIDS denialism, is personally responsible for the deaths of at least a third of a million people, and probably many times that number. Mark Hoofnagle says that:
Denialism is the employment of rhetorical tactics to give the appearance of argument or legitimate debate, when in actuality there is none. These false arguments are used when one has few or no facts to support one's viewpoint against a scientific consensus or against overwhelming evidence to the contrary. They are effective in distracting from actual useful debate using emotionally appealing, but ultimately empty and illogical assertions.
He feels it is defined by tactics rather than by content: "conspiracy, selectivity (cherry-picking), fake experts, impossible expectations (also known as moving goalposts), and general fallacies of logic."
All well and good, but it still doesn't answer the question: why? Scientists may be aloof and esoteric and all that, but why do people affirmatively prefer to believe in nonsense? I just don't see anybody with a convincing answer to that question.