Without God, the basis for morality is subjective. The idea that morality can be deduced by trial and error on what makes a society successful or peaceful is itself also subjective, since "success" itself connotes subjective meaning.
Some cultures have institutional unforgiveness taught and practiced as a norm, and have done so for a VERY long time. They believe that only those that are deserving should be forgiven. Of course if a person deserves to be forgiven then he has earned it, and cannot really qualify for forgiveness.
In Western culture, because of our Christian heritage we put a premium on forgiveness & grace whenever possible. As a Christian, I can state that because I have been forgiven, I am under obligation to do the same. My morality is rooted in God.
Sometimes forgiveness is not possible, true. But the ethic is there looking for the opportunity. The atheist may do the exact same thing, but for different reasons. And, since he doesn't exist for God, he might just as easily change his mind as his rationale changes.
And what do you do when a group of people believe they can only experience peace, when for example they see you and your family marginalized, demoted, or exterminated ? The morality-derived- from-peace model goes out the window, that's what happens. Because, whose peace are we talking about; yours or theirs?