Societies "evolve" in the modern sense of that word: they change, but not necessarily for the better.
Our society might switch to one that is predominantly atheist or agnostic, but there will be belief systems to take the place of religions that have passed. Human beings will always, always have the need for faith because humans will always have the need for hope, and a naturalistic belief system is not superior to other religion in any way. Any problems that religions create - overzealous adherents, hypocrisy, manipulation of people - all that will remain.
If you think that some golden age brought in by scientific purity and an end to religion is coming, prepare to be disappointed. Human nature is the problem, not religion. I sincerely hope you aren't fooling yourself by thinking otherwise; even many agnostics and atheists that post here realize that what I am saying is true.
Truth.
I don't quite think there is absolutely no hope for a peace and harmony fueled civilization, but I absolutely do not see it happening within the next century for sure, but who knows. Social change keeps moving at a rate that I don't think we can predict the future simply using the historical talking points of social progress.
Fairly confident there is going to be something pretty close to fire and brimstone within the next 100 years, we're going to go through some rough shit. It'll hopefully be out of the ashes that a better society emerges.
But the hot button issue: we need to figure a way out to physically evolve our brains, manipulate the genetics to give us less of a need on faith. It's hardwired in our brains, and couple that with other very natural primal behavior on the part of man, it just combines for one nasty solution.
No matter what odd things one chooses to "believe", humanity thoroughly enjoys boiling everything down to "one of us, or one of them". It doesn't matter the topic, doesn't matter the reasons, everything has at least one opposite, and everyone HAS to fall into a camp of certain beliefs. That's our tribal nature, it's what defines more advanced primates from other animals on Earth, and what helped lead to humans. Tribalism helped increase our social capabilities, and we rely on them to continue on. But they are also our enemy, and is what leads to conflicts over so many topics.
We drop religion, surely we'll replace it with something else to feud over.
The best answer is to develop a way to completely unify all of humanity, no more damn inside and outside groups. If everyone treats another like a brother/sister, that will be a huge step. How we can go about accomplishing such a feat, hell if I know.
Major think tanks need to get working on THAT. Sociologists love to create all these pretty sounding theories of how we can move toward a peaceful future, where no man can take advantage of another. That's the wrong approach, because we are human, and as long as we hold progress on a lofty pedestal (absolutely necessary, living as tribes in the mountains is a waste of our capability as a species - we need to capitalize on everything of which we are capable), man will remain more individualistic than community-focused.
Sociology has no clue how to force man to accept everyone as one big group, they just think that's a good idea. We need to figure a way out how to get there, and we can keep many of our same ideals and still accomplish that. Everyone can respect one another like brothers and still compete for progress, friendly competition benefits everyone.