Over on Parableman, Jeremy Pierce argues against the thesis that Muslims worship a different God than Christians. He presents a fairly strong case, but I'm not convinced. The George Bush clone is presented as an example of someone who can successfully refer to the current president even while denying an essential property (his origins). I see it as an illustration that ideas about the history of a referent do not carry as much weight as ideas about that referent's current state. So, the fact that Muslim ideas about the history of Allah coincide in many respects with Christian ideas about the history of God is not enough to override their denial of what God essentially is right now (and eternally); i.e., a triune being.
If the coincidence of ideas about referents were sufficient to make them numerically identical, then Paul's rebuke in II Corinthians 11:4 wouldn't make much sense: “For if someone comes and proclaims another Jesus than the one we proclaimed, or if you receive a different spirit from the one you received, or if you accept a different gospel from the one you accepted, you put up with it readily enough” (ESV). If this other Jesus had beeen presented as completely different, then there wouldn't be a problem. It is a problem because there is enough similarity between this Jesus and Christ to fool the Corinthians. They do not think that they're dealing with a second Jesus, but with the same Jesus that Paul had proclaimed. The apostle is using this opportunity to disabuse them of the notion. The differences between Christ and the Jesus they are now putting up with are enough to constitute different referents, the intentions of the Corinthians notwithstanding.
There is a valid distinction between worshipping a false god and the false worship of the true God. This, at least in Reformed theology, is the distinction between the first and second commandments. The incident with the golden calf while Moses was on Sinai is an example of violating the second. The idol itself was nothing, but they were (falsely) worshipping the true God. Even so, idols representing false gods are also nothing. Paul says as much in I Corinthians 8 when talking about eating food that just happened to be offered to idols. In chapter 10, he is considering actual participation in the offering. He encourages the Corinthians to flee idolatry, explaining in vs. 19 and 20, “What do I imply then? That food offered to idols is anything, or that an idol is anything? No, I imply that what pagans sacrifice they offer to demons and not to God. I do not want you to be participants with demons.” Even though he maintains his position that the idol itself is nothing, he also claims that there is a very real and personal presence behind behind each one. Consequently, while there may be Christians who agree with Jeremy's assessment of their argument that, by denying the Trinity, Muslims “must be talking about a different (and non-existent) being,” I contend that there is good reason to drop the parenthetical “non-existent.” Just as, per his first commenter, it changes everything in his argument if God doesn't actually exist, the same is true if Allah is an extant created being.
Concerning the point that, in claiming that a denial of the Trinity constitutes a denial of the true God, we would have to say the same thing of the Jews, I agree. While I do maintain that the minimal standards for belief in God can change with added revelation, I wouldn't argue that, when Jesus came, “the Jews suddenly were worshiping some fictional being.” Rather, it would seem that the first advent of Christ exposed the presence of those Jews who weren't worshipping the true God at all, even though they were worshipping something. The fact that there were also Jews who were worshipping the true God falsely does not rule out a tertium quid. Moreover, taking it even further, there is no reason to believe that, within the visible church today, all three possibilities don't exist.