Why are religious societies more cohesive?

Reported by the Economist (and discussed on Overcoming Bias), religion brings social cooperation. Attempts to synthesise secular solidarity out of god-free rituals tend to fail. So why is this?

A hypothesis:

Social cohesion is a result of citizens sharing a desire to believe something they all have a tiny private inkling might seem less true if they thought about it too much. They subconsciously know belief is easier when ubiquitously reinforced in social surroundings, and also that their beliefs are more enjoyable than the alternative. Thus they have a strong interest in religious behaviour in others and in their own feeling of unshakable commitment to those who practice it. So they encourage it with enthusiastic participation and try to ensconce themselves as much as necessary to feel safe from reality. If we found conclusive evidence of a god, everyone would be safe, and could get back to non-cohesion; it's the possibility that the sky is chockers with nothingness that gives everyone the incentive for solidarity.

To test hypothesis, compare cohesion across other groups with beliefs (religious or otherwise) of varying tenuousness and of varying importance to their believers.