There would be an existential crisis for those who fervently believed in God, resulting in mass suicides and depression. Some religious institutions would cease to exist, but others would reinvent themselves. (For example, the Biblical stories could be treated as allegories through which to define a secular system of beliefs.) Some would keep traditions alive for the sake of them.
Gradually the old religious institutions would die or morph into unrecognizable forms. People would still find higher purposes to argue about and go to war over.
I'm not one of those atheists who thinks that the end of religion will make the world into a shiny happy place. However, do I think the end of religion would be a net positive? Yes. It is my hope that the new things we would find to argue about would be more substantial and would therefore progress the intellectual evolution of mankind.
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Official Queen ***** of the Universe!