As the saying goes, you will always have good people doing good things and bad people doing bad things. For good people to do bad things, that takes religion.
While some people may think that their belief in god is what keeps them from being a bad person, they probably attribute the good feelings that our brains give us when they behave according to their conscience to god. It's not god, it's millions of years of evolution that's trained us to cooperate towards mutual benefit. Without god/heaven/hell/72 virgins/whatever, there would be (for the vast majority of the population) no motivation to fight the instinct to be good. And as Island Man correctly pointed out - there's a ton of evidence that secular societies are much more peaceful than heavily religious ones. Removing religion removes another thing that divides people and encourages everyone to realize that we're all the same and we're all in this together and might as well make the best of it.