I believe that most here will agree that Muslims do not worship God. But the issue Greear is speaking of is in the area of evangelism and using their claim to worship the God of Abraham as an opportunity to explain the gospel in a meaningful way (as God is a God of means). Reading Greear, I do not see the objections here truly addressing that author's thesis. So while I agree with everyone here that the Muslim notion of Allah is not the Christian God at all, I disagree with some that Greear is supporting that it is.
I think that this is an important enough issue (in terms of evangelizing Muslims...which is the context of Greear's book) to offer a quote from Greear. Whether we agree on his method/understanding or not, it does not seem to me that Greear is saying that God and the Muslim concept of Allah are actually one in the same (which is the direction that this thread seems to be heading).
"This is controversial, but hear me out. Muslims claim to worship the God of Adam, Abraham, and Moses. Many missionaries find it therefore helpful to start with Muslims using the Arabic term for God, “Allah” (meaning literally, “the Deity”), and from there to explain that the God Muslims seek to worship, the God of the Prophets, was the God present in bodily form in Jesus Christ, revealed most fully by him, and the One worshipped by Christians for the past two millennia. This is not the same as saying that becoming a Muslim is like a “first step to becoming a Christian.” And it certainly doesn’t mean that Islam is an alternate way of getting to heaven. It simply means that we are both referring to the only, One deity when we say “God.”
You might ask, “But isn’t the Islamic God so different from the Christian God that they cannot properly be called by the same name?” Perhaps. The question about whether to say that “Allah” refers to the wrong God (or to wrong ideas about the right God) is a highly nuanced one, and there’s not an easy answer. There is no doubt that Muslims believe blasphemous things about God, and their beliefs about Allah grew out of a distorted view of Christianity. The same could be said, though to a lesser degree, of the view of God of the first-century Sadducees, as well as the Samaritan woman, and (to an even lesser degree) the fifth-century Pelagian heretics—not to mention a lot of the medieval Scholastics.
The question is whether the presence of these heretical beliefs (and what degreeof heresy in them) demands that we say, “You are worshipping a different God.” Clearly, the Apostles did not say that about the first-century Jews who rejected the Trinity (even though Jesus said their father was the devil!). And Jesus did not tell the Samaritan woman in her ethnic, works-righteousness distorted view of God that she was worshipping a different God, either. Instead, he insisted that she was worshipping him incorrectly and seeking salvationwrongly. And I’ve never heard anyone say that the Pelagian heretics worship a different God, even though they have been regarded (rightly) as heretics.
At the same time, Paul never said, “Zeus’s real name is Jehovah,” as if the Greeks were worshipping the true God wrongly. So, the question is: is the Muslim view of Allah more like that of Zeus or of the Samaritan woman’s heretical conception of God? That’s a tough question, and one that we need to let the context determine. For instance, many Christians find the use of “Allah” more misleading than helpful. For them, “Allah” falls in the “Zeus” category.
On the other side, however, are many faithful Christians working among Muslims who approach the question of Allah much like Jesus corrected the Samaritan woman. “You are seeking to worship the one God, but you are wrong in your view of him, and wrong in how you seek salvation from him. Salvation is from the Jews.” In my time with Muslims over the years, I’ve found that to be a more helpful starting place. This isn’t driven by a desire to be politically correct, but by a desire to start where Muslims are, and to bring them to faith in the one and only Son of God, Jesus."