If you find such sources, I’m curious what you think it will demonstrate. Will you say that religion is a cause of more socially stable lifestyles?
Because it could be argued that people who are naturally more socially stable are more likely to be attracted to religion (so their faith is an effect, not a cause).
I’m reminded of a “study” conducted by a vitamin manufacturer that found that people who take their product are more healthy than a random sample. The implication is that the vitamins are a factor. However, people who take vitamins are also more likely to eat right and exercise, so the “study” really proves nothing. Only a placebo test (preferably double-blind) could hope to make the correlation - and you can’t do a placebo test with religion!