The Catholic church says of the Muslims that they "acknowledge the Creator and together with us adore the one merciful God." One Catholic apologist added that they have an incomplete view of Him. Does our Orthodox church agree? Or is there debate among the Orthodox theologians on this?
In the opinion of St. John of Damascus, who lived among the Moslems as a high-ranking slave, Islam is a Christian heresy. I understand where St. John was coming from, but I'm not sure that I agree that it is merely a Christian heresy, but rather it is an unholy amalgam. If you look at the history of Islam, you can see where Mohammad basically took elements of Judaism, Nestorian Christianity (a heretical Christian church that existed in the Arabian Peninsula), and local Arabian paganism. You can see elements of this in the Quran, which I have read in its entirety, and in the worship of the Kaaba, which was probably worshipped by the local pagans.
I think the Catholic position is that since Moslems call something God, and there is, in fact, only one God, they must therefore worship God, since there isn't any other God to worship. The Moslems certainly claim to worship the same God; that Christians, Jews, and Moslems are all "children of the Book" but that we refuse to read it correctly. But I think a case can be made that whatever the Moslems worship, it is a false construct, a false god and not the true God. There are Orthodox who would agree with me, and there are Orthodox authorities that would disagree, taking a more "Catholic" reasoning, which, of course, encourages us to "play nice" together. But it is difficult to "play nice" with those who refuse to reciprocate.