That's overly cynical

While a lot of trouble between people appears to be due to religion, those same people could disagree with equal enthusiasm over other issues if they didn't have religion. Leaders find religion a convenient tool, if available. Where it is not available, they can turn some other convenient tool to the same ends. Groups of people can become dangerously enthused over communism, anti-communism, apartheid, xenophobia, nationalism, Trumpism or any demagoguery, fear of almost any kind.
And people of divergent religions can get along. The current Pope and Dalai Lama probably find themselves agreeing on most earthly considerations, though not on the afterlife. When I used to read religious texts from different religions I was struck by seeing that some form of the Golden Rule appeared as a teaching in every one of them if you read long enough to get that far, at least that was true for the ones I looked at. The analogy that stuck with me -- it was from either a Buddhist or Hindu source I think -- it said to envision a circle with the ultimate truth (or call it enlightenment, or salvation) at the center of the circle. People start out at different points on the circumference of the circle. (The analogy works as well if you prefer to imagine a sphere, with people scattered on the surface.) Each different religious path is like a radius leading from the outside, where the people are, to the center, where the goal is. As people follow such a path and draw nearer the center, they also at the same time draw nearer to each other. At the start of the path two people might be completely opposite in their views, and take paths that start very far apart. But the more progress they make on the path toward the truth at the center, the closer they come to each other. Hence people who follow completely different religions find that as they develop in their spiritual progress they find more and more in common. Love your neighbour. Don't kill, don't steal, don't lie.
Twelve gates to the city, you might say.