Yes, but I will say that even if everyone was non-religious we’d still be at each other’s throats over politics or philosophy. You’d still have capitalism vs socialism, conservatism vs progressivism, veganism vs carnism, natalism vs anti-natalism, etc.
Cooperation predates tribalism.
People killed each other before civilizations existed although they were more peaceful. Then again at that time the population density was much lower and we didn’t really have politics outside of “let’s just survive”.
People were cooperative because it was in their interests for survival. Still holds true for today. Rabbits have 9 lives. Why? Because they’re peaceful. They comply. But unlike sheep they can move fast when there’s a predator. Folk wisdom again-predates “history”