A religious person by believing in a higher power has an extra way to self censor, even when nobody is watching. If you do not believe in a higher power that sees all, you can pretend when people are watching, and cheat if nobody is watching, since who will know?
A good example is the internet where one can become anonymous. In this site, the least tolerant are the Atheists. They are always on the attack and cannot live and let live. Those Atheists who vote D, are more likely to lie or promote deception. They are part of a propaganda group who all recite together. You are not obligated to tell the truth or even admit the truth, since you are anonymous. Most will not say the same things to people's faces, since the push back can become real; two faces will not confront one face. Religious people are more vulnerable having one face. They are more honest and easy to bully, since another face is not an option, if it is deceptive.