It it trivial that most religions teach that man is responsible for his own fate, eternal or otherwise. As far as belief and behavior:
http://scienceblogs.com/cognitivedaily/2008/04/22/changing-belief-in-free-will-c/
In this case, we should be wary of using the V&S experiment to argue that belief in determinism has inimical effects for society. But even if it did, I can’t countenance hiding our belief in determinism—a belief shared by Dennett and many compatibilists—from the general public on the grounds that it’s bad for society. That’s simply condescending. The truth is the truth, and shouldn't be suppressed. And, of course, there are some potentially positive effects of accepting determinism and the idea that free will is an “illusion” (i.e., not the dualistic behavior it seems to many people). Those positive effects include salubrious reforms of the criminal justice system and the demolition of an important cornerstone of religion.
Does eroding belief in free will cause cheating? Failure to replicate a famous result.
http://rolfzwaan.blogspot.nl/2013/03/the-value-of-believing-in-free-will.html
I prefer Steven Pinker's thoughts on the subject.