I’ve spent time in Iraq, Afghanistan, Egypt, and other Muslim countries, and I can tell you they don’t worship the same god Christians do. They believe the Trinity is made up of God, a human Jesus, and Mary, his mother. How can they worship the same god?
Granted, Muslims do not believe in the Trinity as we do. Nor do Jews. Yet we all believe in a Supreme Being who created and governs the universe. When St. Paul learned that the Greeks worshipped an unknown god (Acts 17:23), he identified that god as our God. Muslims worship the one God to the degree that they know him—which in our view, is a very limited knowledge.