The Multidimensional Personality Questionnaire (MPQ) is an alternative to the Big 5. In the analyses that I have conducted, MPQ traits have been more predictive of outcomes than the Big 5. I calculated means for atheists, agnostics, those with no religious preference, and all others (sample size = 3,946).
Mean MPQ scores
No religious preference 8.76
Social Potency (likes to take charge)
No religious preference 10.29
No religious preference 12.18
Social Closeness (likes to be with others)
No religious preference 11.03*
Reactivity (easily upset)
No religious preference 6.30
No religious preference 5.74*
Alienation (life is unfair to me)
No religious preference 5.21
Control (plans before acting)
No religious preference 9.45*
No religious preference 6.75*
No religious preference 11.57*
*significantly different from "Others" group
Compared to people who have a religion, those with no preference are significantly less social, more confrontational, less planful, much less traditional, and more danger-seeking. The image that emerges here is a lone rebel.
Turning to atheists, they are less social, less likely to get upset, less likely to think life is unfair to them, much less traditional, and more danger-seeking. Atheists seem like a milder version of those with no preference: solitary, danger-seeking, anti-traditionals who are not confrontational, who plan ahead, and who don't think the world has given them a raw deal.
Agnostics are less social, less traditional, and more danger-seeking. All three non-religious categories have three traits is common: they don't like people as well; they really dislike tradition and authority; and they like risk more than others.
I don't see any necessary connection between disbelief and anti-traditionalism--I certainly did not dislike religion or tradition when I was a skeptic--but they are psychologically like oil and water.