Do we all worship the same God?
The first thing to note is that it's practically a meaningless question. Jews and Christians and Muslims regularly consider each other to be, in some way, getting God wrong. Whether the God they're getting wrong, then, is the "same" one is a distinction almost not worth making.
But then there are folks on the other side of the coin, who want to use our common belief in Jehovah as some sort of banner. Pretty much anything that comes before or after the phrase "After all, we all worship the same God" is guaranteed to be a wish for peace that is quite simply unrealistic: such people are either naive or haven't been paying attention. If we're ever to have complete peace among folk of different religions, it won't be because we've all suddenly realized we "worship the same God." Catholics and Protestants in Northern Ireland worshiped the same God.
As did Cain and Abel.
That last fact should take us to where we belong: that brothers and sisters and cousins draw blood from each other is an underpinning of the Abrahamic faiths. It's built into the very worldview of all three religions (as well as most other religions) that humanity will be in sin and conflict for a good long time.
Nonetheless, it's important to separate fact from fiction and fancy.
Some say that the spiritual world is bursting with thousands of deities and semi-deities to be aligned with or mollified (Hinduism, pre-Islamic Arabic religions); some say that we are the pawns of a band of gods and goddesses who align with or against each other (Greek, Roman, Norse religions); and some say that there may be no gods at all but rather there is the world and we can either align ourselves with it or not (Buddhism).
Then there are folks who say there is one and only one God, the creator and sustainer of all that is, the summum bonum, the unmoved mover that exists beyond our cosmos and created it ex nihilo, who made Adam out of clay, who brought Noah through the flood, who made himself known to Moses, who makes himself known to man through his revelation (rather than some mystic divination on the part of man), and who can for lack of a better term be called "The God of Abraham."
Among those folks are the three great Western religions: Judaism, Christianity, and Islam. That's right, Western. All three are part of the Western tradition of life and thought, and all three are what we would now call Middle-Eastern in origin. Think of two distinguishing marks of the West: one, a confidence that a single omnipotent Creator has created an orderly creation that can be explored and understood, leading to an explosion of understanding and exploitation of the natural world; two, a confidence in humanity's place as over-and-above, leading to [in our best moments] a sense of responsibility toward the natural world and to a placing of the human at the center of art and literature — and, in the Christian world, a placing of the human figure at the center of visual art. It's easy to see that these three religions have ineluctably shaped the West.
Now, it's obvious that Jews and Christians and Muslims have divergent beliefs about the one true God. Indeed, even within each of those groups there are divergent beliefs such that one can truthfully if only poetically say that my wife and I "don't worship the same God," although we would affirm that beyond the level of idiofide we most certainly do. But, even with those divergent beliefs in mind, it's a bit acrobatic to say that Muslims and Christians and Jews don't worship the same God.
Certainly the God of the Koran is different in many dimensions from the God of the J account or the God of St Paul's letter to the Romans; no more different than is warranted by the divergent relationships God institutes with Ishmael and with Isaac. But those relationships are surely no less real for being divergent. And the nature of those divergences is in fact covered right in the scripture that Christians and Jews call sacred. Remember that God promises Abraham he will be the father of great nations; Abraham, in his old age, and with an old wife, takes the initiative of fathering Ishmael with his servant Hagar. Then he has a legitimate son, Isaac, with his (still old) wife Sarah. So both diverging lines carry the blood of Abraham, and both are the fulfillment of a promise to the "father of nations," though Christians and Jews believe that the offspring of Isaac carry the primary covenant. The children of Ishmael and the children of Isaac have been at war ever since.
Exactly who is the Jehovah we worship? We can note that Genesis 16 and 17 and 21, which touch on God's relationship with the Arab people, indeed his covenant with them, are not only part of our shared history but part of our (Christian, Jewish) vision of the character of God.
Here we have a clear picture of God saying to Hagar that he hears her affliction and will have his own way of caring for Ishmael and seeing to his descendants, promising to make of them a great nation, assuring Hagar and Ishmael (and Abraham) over and over that, in that distinctive repeated phrase, he hears them. In the face of such a promise, I find it difficult not to hear the shrill voice of Sarah ("Cast out the son[s] of this bondwoman!") in much of our modern discourse.






