Okay, first let's all remember Frazer's rules of sympathetic magic: similarity, and contact/contagion. The rule of similarity entails that an object may take on properties of another object by virtue of being very like the original object in appearance ("like produces like"); whereas the rule of contact/contagion entails that the object takes on these properties by virtue of having been in contact with the previous object, long after the contact has ended. These rules appear to be intuitive, and take effect in various ways. For example, a person might be disgusted by a brownie that resembles a turd, and refuse to eat it (similarity), or refuse to drink from a glass that once contained a cockroach, regardless of how thoroughly or frequently it has been washed since (contact/contagion). We intuit that properties transfer in ways that they actually don't, which produces some understandable (since we share intuitions) but illogical (since they're not actually based on anything) conclusions about what it's okay for us to look like, consume, or otherwise associate with.
The notion that negative spirits, or demons, are behind this association-- that they are, in fact, the association itself-- is just one step further, really. The religious step. Because religion puts agency behind everything. Most importantly, it puts agency behind what is important to us. What we value. What we feel. What frightens us. What we love. If you demanded that I define religion for you, I would...probably do so a lot more readily than a lot of people who study religion academically. But my definition would go something like "A practice of systematically placing non-human but human-like agency behind our most important intuitions." That's a little more elaborate than Stewart Guthrie's "systematized anthropomorphism" and also more specific than and contrary to Pascal Boyer's minimally counter-intuitive concepts, because Boyer thinks that traits such as invisibility and non-corporeality are counter-intuitive notions about an agent. I think they're intuitive. I think that we perceive invisible, non-corporeal agency all of the time and probably have evolved to do so, and that demon-infested clothing is just one tiny, apparently ridiculous* but not actually unique or even very unusual manifestation of this tendency.
I'm looking forward to reading Robert McCauley's book Why Religion is Natural and Science is Not, because I'm interested to hear his take on a now common refrain among cognitive scientists of religion, which is that perceiving agency in the world around us, behind unusual but significant events, behind our existence itself, is all-too-human even for the most secular of us. But subjecting supposed facts to rigorous testing and objective examination really isn't-- we are certainly quite capable of it, but it has to be learned. This is no longer an alarming hypothesis to me, and in fact it would take quite a lot of evidence to convince me that it's not true. But the alarm really seems to stem from a notion that the intuitive is somewhere inherently more trustworthy, more insightful (see "women's intuition") and the counter-intuitive wrong, while nothing could be further from the truth. Intuitions exist for reasons, but after all, those reasons are not necessarily ours.
*Ridiculous, I think, because of the mundane subject matter. Not even the most materialist of us would be surprised to hear that someone associates supernatural agency with, say, an amulet or a relic. We might not believe it ourselves, but we're familiar with the concept. Clothing from Goodwill, by contrast, is about as ordinary as it gets, so Robertson suggesting that demons might be attached to it sounds as superficial and weird as praying for a good parking space. But if there are supernatural agents out there who are interested in our lives, the postulate that Robertson accepts and many if not most religious people do as well, why should this interest not extend to such things as parking spots and laundry?