This doesn't really help me out. You seemed to be suggesting that the three religions couldn't possibly be worshipping the same God if they held inconsistent views on Her. If A thinks B has a son, but C thinks B doesn't have a son, that doesn't mean that A & C aren't both talking about B. It just means that at least one of them is wrong.
Yeah, as an atheist, I can think of them as obviously separate theoretical constructs with just a lot of overlap. Muslims give God features that Christians don't, and since both faith 'defines' their gods, that's just fine.
If I believed in either entity, then it would be simpler (and probably more correct) to say they both worship the same god, but that there're a series of mistakes being made in their conceptions. I mean, I love my aunt despite the fact that she had an affair. My uncle loves her, not knowing that she did. We both love the same person. But that requires her existence.
I now completely understand the point you guys were trying to make.
So there are actually at least 3 Gods that pranked Abraham into almost killing his son?
Actually made me laugh out loud. Troll god.