... do not worship the same god.
Just because a particular religion believes there to be one "real" god, doesn't mean they all happen to acknowledge the same god as being the one. You don't suppose that all polytheistic religions keep the same pantheon, do you?
Just because modern day Judaism, Islam, and Christianity claim a connect to a guy named Abraham that people said the (singular) god spoke to doesn't mean it's true in any case.
Here's a bit of Christian Theology 101 for us to consider: Christians don't believe in "God." (Well, I don't, anyway.) Christians believe in the Trinitarian god who is Father, Son and Holy Spirit. Christians do not say, here is an idea of "God." Jesus is divine, so our idea of that "God" will tell us what Jesus is like. No, no, no! Christians believe that Jesus fully reveals the Trinitarian god: the tradition we have received about Jesus, the second "person" of the Trinity, is the foundation of any ideas we're going to have about "God."
Therefore, any statement about "God" that doesn't start with "Jesus is/was _________ so therefore God is _________," is opposed to any Christian theological statement. And yes, it is needful and right to move on and talk about the connection of that god to the god of the Old Testament, and even to use "reason" to sort out what that god might be like, but there is no valid starting place in Christian theology other than Jesus.
Any god that cannot be said to be like Jesus the Christ, and manifested in Jesus the Christ is a different god than the Christian god. Any god that is not understood as three persons in one substance is a different god than the Christian god.
That does not mean that other religious folks who worship these other gods are bad people. I don't hate them. I certainly don't dislike them for that reason, either. I would never be unkind to anyone for that reason. It doesn't mean we can't have inter-faith dialogue, and it doesn't mean we have no common ground at all. It just means that we worship and serve different gods.