Here are the issues we have. There’s debate on whether Christians and Muslims worship the same God. One side says they do not, that Christian’s and Muslims have such a radically different view of God that when either one of them is speaking about God, they are literally talking about two different beings. It’s not just a case where they are talking about the same being but just have a different view or opinion or disagreement about his characteristics. But their disagreements are so fundamental and deep that it displays that they literally are referring to two separate entities entirely and are worshiping two different beings. Two issues that come up is that, if we want to be consistent and honest, we need to ask the question if Christians and Jews even worship the same God then. This would cause some issues because of the intimate relationship between Christianity and Judaism. Islam also claims that the God they worship is the same God we see revealed in the Old Testament. This also then brings into question of whether Muslims and Christians and Jews are even referring to the same Jesus. Their understandings of him are so radically different maybe we should say they aren’t even talking about the same person, but for some reason that doesn’t seem to make sense in the case with Christ, but then we think it makes sense when talking about God (either the Father or trinitarian God).
The other side says that all three religions are referring to the same God but just have different understandings of him. The issue with this is there’s a real question about how much you can disagree and differ on a description of something, but then still be talking about the same thing. Like how much information can someone have wrong about you before you decide they are no longer even talking about you but someone else, what sort of information do they need to get wrong before you decide they are no longer talking about you but someone else? When it comes to God, Christians understand God as a trinity and so charge Islam and Judaism as distorting the very nature of God. This distortion is quite large and does give merit to the claim that Jews and Muslims don’t even worship the same being because their conception of him is so fundamentally different. Beyond that, Christians and Jews have an argument that their understanding of God’s interaction in history is different than that of Muslims and suggests that they are referring to two different beings.
This issue is quite important because it does have an effect on how we do interfaith dialogue. If you think your religion and a different religion worship the same being but just understand him differently, this gives more common ground than if you think the two religions are worshiping two different beings. In my humble opinion, it seems that all three do worship the same being but have different beliefs about this being. I think the history they share of this being is hard to ignore and suggests they are referring to the same being. Also, I do think the conceptions they have of this being are similar enough and contain essential enough details that we can say that the differences they have is more of a difference in some of this being’s characteristics than it is that they are worshiping a different being entirely.