As I often say to my students when breaking down some counter-intuitive but astounding fact about the natural world, "I can't make this stuff up." Dawkins is on to something here: there really is something seemingly magical about reality, in that it often defeats our expectations, which are so grounded in our day-to-day experience. When we encounter phenomena at scale different from ours, they really do seem to violate our sense of what the rules are. This is part of the appeal of magic, in that sleight-of-hand tricks and optical illusions are used to elicit a sense of "rule violation". We are amazed and intrigued, and we wonder "how do they do that?"
This is a healthy sense of "magic", the sense in which apparent rule violation elicits wonder and inspires the thoughtful to attempt to figure out the secrets behind Nature's tricks. In science, we proceed most fruitfully when we assume that there is, in fact, a natural explanation for natural phenomena and develop proposals ("the hypothesis") to explain the phenomena. What makes the hypothesis scientific, by the way, is whether or not it can be tested via experiment.
Of course, there is another meaning to the word "magical". That is when a person assumes that the phenomena in question can not be explained naturally, and requires that the trick not be explained in terms of Nature's rules, but in terms of those rules being violated. Otherwise intelligent and educated people do this all the time when they encounter phenomena or other ideas that run counter to their day-to-day experience, and often feel that they are exercising "common sense" when they embrace a supernatural cause. "Embrace" is the right word, because once you are emotionally invested in the supernatural claim, it becomes difficult to look at the evidence dispassionately. I claim that once a person is so invested, they have adopted an unhealthy sort of "magical thinking", which places them on a collision course with reality and makes them more willing to affirm things that are ludicrous on their face.
Here's an amazing example of this. There is a recent phenomenon (mostly in the Midwestern United States) of flocks of birds falling dead, out of the sky, by the hundreds in some cases:
Well, this is obviously a natural phenomena that seems to violate our expectations, and it certainly cries out for explanation. Scientists are conditioned by their disciplines to seek natural explanations for natural phenomena, and it is a truism that such an approach is the only one that proves rewarding in scientific terms. So, naturally, scientists have proposed different ideas to explain the phenomena of birds falling dead out of the sky. They will gain support to the degree that they can be tested. That's the scientific response to anything that looks like magic: assume a natural cause, come up with creative ideas that can be tested, and see how the ideas perform.
Or, you can do the unscientific version, and assume that anything that looks like magic really is magic, the act of a supernatural being. So if birds drop dead....it must be God killing them. Why would God do that? Well....check out this video and get the skinny from Cindy Jacobs, a Weatherford, Texas woman who helps lead a ministry called Generals International, and who is actually regarded as a "prophet" by the Apostolic Council of Prophetic Elders. Members of this group (whose political influence is growing) believe that they are engaging in spiritual warfare, and that natural disasters are signs of God's judgement, so they are preconditioned in a sense to regard the following idea as plausible: according to Jacobs, flocks of birds falling dead out of the sky is caused by a change in government policy regarding gays in the military. That's right, God kills birds because we no longer expect service people to "Don't Ask, Don't Tell."
This is an example of the sort of "magical" thinking that science can't do anything with, because it's something we can conceive---but can't test.
It's conceivable that a supernatural being could've killed birdies because our government has dropped a policy that requires gay service people to keep their orientation under their hat, because, don'tcha know, the supernatural being hates teh gay. It's also conceivable that a supernatural being loves gays and hates gay-baiting ninnies, and so the supernatural being killed the birdies because our government doesn't do enough to promote teh gay.
Both of these ideas are conceivable, but neither are testable in a scientific sense. Both are pretty ridiculous. Why would God kill thousands of blackbirds in Arkansas to protest gayness? I mean, if a thousand pink cockatiels fell out of the sky over Castro Street, it might seem a little more on-point...but from a scientific perspective, all such explanations are still equally untestable, and worthy of scorn.
What about a non-scientific perspective? Well, all of us have them. We also have a tendency to mix all of our non-scientific perspectives together. We jumble together our personal interests, our cultural concerns, our ethnographic history....and our personal beliefs about the supernatural. We invest in them, and to the extent that we are unable to think objectively about them, we become capable of not just believing things which can't be tested, but acting as if others should kow-tow to things that, while not actually demonstrated, seem unquestionably true to ourselves.
Me, I believe His Eye is on the Sparrow, but I don't go around expecting other Christians to believe that Yahweh would capriciously punish our country by making birds drop dead---and, by extension, I am reluctant to regard gay people as my natural enemies. It's not a plague, nor is it something that most people who identify as "gay" would choose, given that people like Cindy Jacobs treat them as lepers.