"is it possible, even in theory, for each religion to have its own God?" Every religion is a theory, so the question is moot. Every religion is a set of conjectures and unsubstantiated claims regarding the nature of a supreme being that has never been proven to exist. (Even if we suppose it did exist, theories about its nature and will are still speculative). So, there are a bunch of competing theories, each making vehement assertions about their ideas - quite like a shouting match. Buddhism and Jainism are exceptions - they are atheistic religions (there is no congnizant God in these religions).
I read a T-shirt slogan a few months ago that was quite hilarious - It had a picture of a holy book (which I shan't name, but you can use any religious book there), and below was a statutory warning: May impair judgment. I think that gives you the idea...
Karl Marx astutely noted that religion was the opiate of the masses. A fundamentalized religion is like the heroin of the masses... So, no, it's not surprising at all to see people fight over ideas that have no factual basis - I'm told drug addiction can make people act irrationally.
