I agree with Faith that the Gods of Christianity, Judaism, and Islam are not logically equivalent. The Islamic God does not have the Jews as a chosen people, and the Jewish God does not have a son - that should settle it right there, they are not exactly the same concept. Of course, the God worshipped by Christian A, and Christian B are also likely to be different on some level as well.
Since God is usually defined to be incomprehensible in some regards, couldn't we say that everyone has an incomplete understanding of God? What if the differences between Allah and Yahweh are minute in comparison to what is unknown about God?