I think the general population is guilty of magical thinking, at one time or another, like Marc said.
And, I'm going to say something controversial, here, even as a "person of faith". I also believe that many, if not most people who pray, have acquired the bad habit of reducing it to a mere act of magical incantations. Listen to yourself pray, if you do. Listen to those who do pray. There is a very repetitive nature to it all; a constant asking for protection, asking for healing, asking for coverage, asking for blessing. It is a continuum of requests to change the course of nature and our lives. It is really akin to white magic, cloaked within a different verbiage, and under the guise of a different line of spirituality. But all is an attempt to provide us with a false sense of security - that we will be exempt from adversity.
In the secular realm, this can come in the form of OCD. Even as a small child, if a stranger accidentally touched me, or rubbed up against me, I had a repetitive formula that I'd say, secretly, in order to clear myself of any germs or negativity related to that person. This gave me a false sense of security, but what did it change? Nothing really. And with health anxiety, I have found, like many others here, that we become entrapped with thinking that worrying and reassuring will protect us from the diseases that we fear. Or, even more ironic, that if we stop worrying and feel good for once, our worst fears will come to pass! All of this, in my laymen's view, is a false sense of security.
A philosopher once said, "Infinite resignation is the last stage before faith". Basically, I think this means that we really do have to give up, give in, and let what will be, be. I'm struggling with that quite a bit, and have a long way to go. Until then, I'll probably just continue to be anxious.