I think belief in god (higher power) and some sort of punishment in the afterlife is what holds much of society together.
We as a society are still barbaric in many ways and have not matured to the point of knowing right from wrong with out guidance or being motivated to do right and not wrong without the threat of punishment.
"Good people do not need laws to tell them to act responsibly, while bad people will find a way around the laws" -Plato.
What ever these studies are, I think you'd have to take them with a grain of salt as we don't know how a society would act and behave if GOD was ever proved to not exist and that we are just animals who actions will never be held accountable after we die.
I disagree.
I don't see much religion where I live, and there is less than 300 murders every year in the whole of Sweden, that number has been consistent since the 70's.
What has been shown to have importance however, is to have a civic society, that we socialize in organisations.
Robert Putnam showed this with a study of the difference in democracy levels in northern and southern Italy, where in Northern Italy, for centuries people had been organised in choirs, football clubs, church clubs, and various forms of social activities.
Whereas in southern Italy, they had not, and the level of democracy (voting numbers et al) where much lower.
There is also a book, Bowling Alone, which deals with how the foundation for democracy in USA is eroding, where in the past Americans were spending time together, eg bowling in clubs, but nowadays spend more and more time on their own, in front of the TV.
Very interesting book.
I believe Putnam has a point, and that it is the lack of socializing that could lead to a downfall of a society.
Not whether or not a society is religious.
Eg, look at Iran, a very religious society. And far from a democracy.
Another example, related to Christianity: Look at Spain in the 60's and the 70's. Christian. And a home for fascism. And France, England, Germany and many other countries in the 19th century. None of them were democracies.
But they were all Christian nations, and very religious.
So there is no correlation between a high level of democracy and a high level of religiousity.
I would rather say that fanatism is one of the factors that effectively prevents democracy.
But organised socializing will definitely help democracy. Check out Putnam's work.