I think the opposite, in that when you look at the moral teachings of the great religions, it becomes rather striking in just how much they agree with each other. As to the morality of the non-religious you misunderstand the question. It is not that the non-religious by being non-religious necessarily become evil people but that their denials of a transcendent order leaves us with nothing but a subjective relativism. And this relativism has lead to great evil. In the United States alone, from 1973 to today around 50 million lives have been snuffed out before any of them could take their first breath. All that human potential thrown away usually for the convenience of those lucky enough not to have been denied their lives. What a crowning moral achievement of our enlightened secular times.
Now granted, to blame the non-religious for this alone would be unfair. Everyone is complicit in the greed, selfishness and narcissism of our current times.
If subjective relativism is the true state, which I would say it is, then we will be at conflict with each other as long as those who see their particular objective morality being THE one, and particularly when many religions will be fighting to keep their powers over their flock and inevitably coming into conflict with the other religions. It's hardly striking that all the religions tend to agree as to morality, simply because most humans do anyway, and where the religions just built on any existing morality. We would hardly have progressed as to forming ever larger groups if this wasn't so. Even if our earlier ancestors had any religious beliefs, these would probably not have been set out so as to dictate or influence morality much. That came later with the monotheistic religions and perhaps others.
And I think your view of our current state is just being selective. People will behave how they will dependent upon the circumstances in which they find themselves, and we just happen to live in very changing times and where our actions are not fully understood until later when any damage done has become more obvious - like our consumer societies, built on this myth of endless growth.
You've never watched an action movie?
I had a revelation some time ago. I walked past the TV as others were watching "Guardians of the Galaxy" and I saw a scene where this blue alien thing was using some kind of magic homing bullet device to mow down countless goons and henchmen while silly music played over the top of it all. And it struck me because while the scene itself was not particularity graphic the way it portrayed the merciless killing of dozens upon dozens of men as something entertaining left me with an almost nauseous feeling. There was something almost psychopathic about it. There was no hint of reflection about the moral magnitude of what was depicted. We're just meant to cheer as the blue alien thing butchers his way through the goons.
And so I recall a story my mother told me. When my grandfather bought his first television my great-grandmother supposedly spoke up and said to him: "You have brought Satan into this household". I think there was wisdom in that old-timer. She saw what we do not. That the modern mediums of media while not evil in themselves nonetheless are of great service in the propagation of evil attitudes in the culture. An example of this... How many music videos these days are little more than soft porn and what does that teach people - particularly young girls - about what to value?
Well I think there is too much violence on TV, and no doubt elsewhere, and I have watched my fair share over the years, but the motives for watching such can vary so perhaps much of this is not really reflecting the violence in societies but more stoking it. I'm not claiming that there isn't a violent side to human nature but that it is not something inherent in all and often only comes out when they are threatened by others. The increasing population issue, and living in such dense communities, seems to be one that does so, apart from the appetite to be excited and/or challenged by aspects that violence tends to throw at one.