I don't think that's generally true. Sometimes, but not usually.I would suggest that the belief in God will help people to do what is right.
Most people learn to do the right thing, usually. But the best way to get otherwise decent people to do atrocious things is some kind of ideology. Some idea that is more important than humans and the human situation. Religion often fits that. Other ideological world views can have the same unpleasant results. Like Communism and Capitalism.
I think that the main time religion helps people be moral is when they're taught that it's important to be moral, or God will catch you and punish you. The problem with that is that if their faith wavers, they might do almost anything. Or if they believe that God approves some atrocious behavior that it's OK. Giving people a more solid moral foundation, like "Moral behavior will work out better for you, here in this temporal world." isn't something traditional Abrahamic religion is good about teaching.
Tom