Much has already been written about the Wheaton professor who — perhaps trying to make a mainly human rather than mainly theological point — prompted a furor when she asserted that Christians and Muslims worship the same God. The question is complex, and has been discussed profitably many times in the past.
Here is an excerpt from a thoughtful (and irenic) article by Timothy George, published in the aftermath of 9/11:
Is the Father of Jesus the God of Muhammad? The answer is surely Yes and No. Yes, in the sense that the Father of Jesus is the only God there is. He is the Creator and Sovereign Lord of Muhammad, Buddha, Confucius, of every person who has ever lived. He is the one before whom all shall one day bow (Phil. 2:5-11). Christians and Muslims can together affirm many important truths about this great God—his oneness, eternity, power, majesty. As the Qur’an puts it, he is “the Living, the Everlasting, the All-High, the All-Glorious” (2:256).
But the answer is also No, for Muslim theology rejects the divinity of Christ and the personhood of the Holy Spirit—both essential components of the Christian understanding of God. No devout Muslim can call the God of Muhammad “Father,” for this, to their mind, would compromise divine transcendence. But no faithful Christian can refuse to confess, with joy and confidence, “I believe in God the Father. … Almighty!” Apart from the Incarnation and the Trinity, it is possible to know that God is, but not who God is.
Timothy George, “Is the God of Muhammad the Father of Jesus? Christianity Today (February 4, 2002) (link).