It is estimated that there are around 1 billion secularists in the world, or about 15% of the total world population. This is smaller than the largest religions, but larger than most religions. What's more, these numbers seem to be growing. We may never reach a point where secularists are a majority, but we are approaching the point (or have reached it already) where secularists and secularism needs to be taken more seriously.
Boston University's Catherine Caldwell-Harris is researching the differences between the secular and religious minds. "Humans have two cognitive styles," the psychologist says. "One type finds deeper meaning in everything; even bad weather can be framed as fate. The other type is neurologically predisposed to be skeptical, and they don't put much weight in beliefs and agency detection."
Caldwell-Harris is currently testing her hypothesis through simple experiments. Test subjects watch a film in which triangles move about. One group experiences the film as a humanized drama, in which the larger triangles are attacking the smaller ones. The other group describes the scene mechanically, simply stating the manner in which the geometric shapes are moving. Those who do not anthropomorphize the triangles, she suspects, are unlikely to ascribe much importance to beliefs. "There have always been two cognitive comfort zones," she says, "but skeptics used to keep quiet in order to stay out of trouble."
Only a small portion of secularists are as radical as the "strong atheists" championed by British evolutionary biologist and author Richard Dawkins. The majority are more likely to be indifferent to religion or mildly agnostic, according to Kosmin's analysis. There are also secular humanists, free thinkers and many other factions. "One problem of atheism research is that we simply can't agree on a unified terminology," notes Kosmin. "Every researcher thinks he is Linnaeus and invents his own labels."
Then he tells of a meeting of secular groups last year in Washington. They were planning a big demonstration. "But they couldn't even agree on a motto," he says. "It was like herding cats, straight out of a Monty Python sketch." In the end, the march was called off.
It seems implausible to me that there would be any particular way of thinking that is common to religious believers and another that is common to secularists -- especially in the way described above. First, and perhaps most important, is the fact that the religious/secular distinction is not the same as the theist/atheist distinction. There are atheistic religions and there are secular theists.
Second, even if we focus on religious theists and secular atheists, the mere fact that one is a secular atheist doesn't mean that they reject "agency" in the world around them. There are secular atheists who believe in ghosts, ESP, astrology, and a myriad of other things that would give them a mind-set or approach that may be rather similar to that of religious believers.
The fundamental problem is that "secular" and "atheist" are far too broad to easily generalize, especially when it comes to minutiae of psychology -- and the same is true of "religious" and "theist." The best one might be able to do is generalize a little bit about a subset of secular, skeptical, critical atheists in the modern west. And while the overall size of that group may be big enough to study, finding enough to create a reasonable sample size may be tough.