Clearly their religius views are so different that they need to fight, even though them being religius sects imply that they branched off from an original matrix religion. And their fighting absolutly has nothing to do with them wanting political, economic, and social hegemony in Iraq, clearly.
And they want this political, economic, and social hegemony for their own sect and not the other because? It's because their religious views are different from each other, it doesn't matter that the differences are so small and therefore should theoretically not be worth fighting over, the fact is it's happening.
The big 3 religions start with abraham but I wouldn't consider them very similar anymore. When small differences are what stops certain sects from getting to heaven and as a result, enduring eternal torture, the fact that they branch off the same matrix religion means little.