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I would say you are in the right line of thinking when it comes to war/religion.
However, the I would say that religion plays a very large secondary role.
Religion is used to divide people. This is built in. If one group of people believe in God X and the other group believes in God Y, they have made themselves into subsets of humanity.
It divides in the same way that "race" or "ethnicity" divides. These divisions are the kindling of war and hate. What makes religion such a big problem in this regard, is that it can divide in an even bigger and deeper way.
When Group X is taught to believe that Group Y is "evil", follows "evil", or at the very least is sinful and wrong...it is not conductive to unity and peace.
In some cases this leads to creating ethnic wars...that are based on religion. As was the case in Yugoslavia, in WW2 and Today. A Serb and a Bosnian were the same thing, they were both Serbs....but one group of serbs was orthodox while the other group of serbs was muslim. If you were serbian and muslim, you became Bosnian. So while the war was "ethnic", the only reason they were even seperated to begin with, was different religions. They had the same language, food, costumes, you name it....but were separated by religion, and that made it possiable to create the US vs. THEM needed for mass murder.
I remember reading a news article at the time that said a group of Bosnian Serbs (See how silly this is, they are serbs, who are orthodox, who are from Bosnia. As opposed to Serbs who are muslim and from Bosnia who become bosnians), had raped a woman, and told her that "she would have Serbian Babies". Think of how silly that is.... Are the babies going to come out orthodox?
A similar thing happened in WW2. The Nazis were experts at exploiting religion, to meet their more racist/imperial goals.
They created Catholic SS units and muslim ss in Croatia and Bosnia to kill Orthodox Serbs, because the Serbs rebelled against the Axis. The Italians were Catholic...The Croats were Catholic...so the Italians said you fight with us ("fellow catholics") against those scum orthodox serbs.
Today, as though history, there are more examples of this tribalism than can be counted.
Think of how much more easy it is to get otherwise rational people to want to fight each other, when you divide them into competing tribes. When it becomes "Those darm MUSLIM arabs" or "those CHRISTIAN americans", makes it a lot more easy to kill the evil other.
What makes all this tribalism so heart breaking for non believers, is that it is over nothing. It is over imagination and stories.
It is not just the occasional killing in the name of that is so heartbreaking and counter productive to humanity;
It is the deep seeded separation.... Which is all the worst, since there is no good reason for it.