Interesting thoughts here, from Dr. William Abraham, of Perkins School of Theology:
"My thesis is this: Christians and Muslims believe in the same God; they do not worship the same God. Christians and Muslims can both identify their God as the one and only Creator of the world who is all good, all powerful, and worthy of worship and obedience. Both Christians and Muslims believe that this God exists; they disagree with atheists and agnostics on this score. Both Christians and Muslims are realists with respect to truth."
[...]
"In the context of worship Christians insist on the identity of God as laid out in the Apostles' or Nicene Creed; they speak of God as Father; they name God as 'Father, Son and Holy Spirit.' The practices of the Church show that we pray to the Triune God, that we baptize in the name of 'The Father, and of the Son, and of the Holy Spirit,' and that we praise God as the Triune God.
"These are not incidental phrases; they are canonical; they are constitutive of the identity of God in the Church. All of this is resolutely, systematically, and canonically rejected by Islam."
Abraham said that these differences cut so deep that in this context, it is natural that we do not worship the same God. [...]
Abu Daoud says: it seems like he is trying to go half way between the two temptations of denying that Muslims believe in the true God AT ALL, and the other one of pluralism in saying that they do believe in the true God AND worship him rightly.
