I almost put this on my Facebook wall but decided it fits here better:
It is important to recognize the difference between the way that the "newer" religion looks at its concept of God and the way that the "older" religion looks at the "newer" religion's concept of God. Just as it is understandable that a Jew who has not converted to Christianity believes that the Christian and he do not worship the same God, and this does follow from his premises, so it is with Christianity and Islam. The Muslim, whose religion changes the concept of God in important ways from that of the Judeo-Christian tradition, claims that there is an essential continuity, but the Christian, as long as he remains a Christian and not a Muslim, should reject this.
In the same way, the Christian insists that the Trinity is not a change in the concept of God and is consistent with Judaism, but unless a Jewish person converts, he believes this to be false. As soon as a modern Jew decides that the Trinity is not that big of a deal as compared to his previous concept of God, he to some extent has accepted Christian ideas. This fundamental asymmetry between the way of viewing the question from the perspective of older and newer religion must be understood and maintained.
That is why, recognizing the important innovations in Islam, we as Christians should hold that we and Muslims do not worship the same God. That Muslims say that we do is not the determining factor, because we aren't Muslims.
No theories in philosophy of language get around the need to decide how important the differences are between the Muslim and Christian concept of God. And if they are sufficiently crucial, then we should not say that Muslims and Christians worship the same God.
Update: Some have tried to make an analogy to cases of what is called "opacity of reference." For example, Clark Kent and Superman are the same person even though Clark Kent's co-workers don't know this. The morning star and the evening star are the same heavenly body, and this is true even if someone thinks that they are different. But this analogy, if anything, tells us that the Christian definitely should disbelieve that Muslims and Christians worship the same God, though Christians can believe that the God of Abraham is the same God that he (the Christian) worships. In the latter case, Christians believe (though modern, non-messianic Jews deny) that the same Being caused the origins of Judaism--the promises to Abraham, the Exodus, etc.--and the origins of Christianity--the resurrection of Jesus, etc. In that sense, the Christian says that the God of Abraham is the same entity as the God we worship, just as the morning star really is the evening star. But no Christian should believe that the God whom Jesus represented is the same entity who caused the origins of Islam! On the contrary, we as Christians should emphatically deny this. That point alone puts paid to any attempted analogies of the problem to that of the morning star and the evening star. It also distinguishes what the Christian claims about the relationship of Christianity to Judaism from what the Christian believes about the relationship of Christianity to Islam. The point is not that only a Trinitarian can be in some sense worshiping the true God. Abraham was not a Trinitarian but was worshiping the true God. But Abraham, we believe, really was in touch with the true God. The true God really was the source of Abraham's revelations. The true God was not the source of Mohammad's.