Do Christians and Muslims worship the same God? Interesting question. I once delved into a similar question as to whether the God of Moses and the God of Abraham were one and the same? Based on a strict comparison of the mitzvot described in Genesis vs. the mitzvot in the other four books of the Pentateuch I came to the conclusion that they were technically consistent with each other, even though there was an undeniable tension between them — with the God of Abraham (a just judge of the earth who judges all men by their deeds irrespective of person) emphasizing the universal aspects of the Hebrew faith and the God of Moses (the special protector of Israel) its more tribal aspect. I also hypothesized that the tribal conception may have been necessary for the universal conception to survive, and that that tension has continued to exist throughout Jewish history.
Anyway, it is all laid out in an article I published in the journal Judaism, “The Torah and the West Bank” (Summer, 1987). Look it up, Mr. Mead. I think you would enjoy it.