Akwat, then what do we say about the different views of Catholics, Baptists, and Mormons? To put it roughly, Catholics believe priests are a necessary conduit to God, that saints may be prayed to, that relics and idols have some importance, etc. That isn't reconcilable with the protestant view of God.
That there are variations, even major variations, is beyond dispute. But be careful not to conflate categories. Most of the differences between, say, Catholicism and Protestantism fall under the categories of Soteriology and Ecclesiology, not Theology Proper. As far as the ontological description/definition of God is concerned, both groups subscribe to Nicene Trinitarianism and Chalcedonian Christology; hence, their views on who/what God is are substantially identical. (Specifically: There is but one God in essence who exists eternally in three distinct Persons--Father, Son, and Holy Spirit. Also, Jesus is conceived of as truly God and truly man, one person yet two natures, the two natures being united without confusion, mixture, or division.) It would be completely accurate to say that the Catholic and Protestant views on salvation and the nature of the Church are mutually exclusive, but not that their views on the nature of God are mutually exclusive.
Now, as for the Mormon view of God, that's a little different. I don't profess to know as much about Mormon doctrine, but my present understanding is thus (Ender can correct me if I'm mistaken on anything): The Church of Jesus Christ of LDS sees itself as a Restorationist movement. That is, it holds that Christianity committed wholesale apostasy shortly after the Apostolic era, and adopted doctrinal stances contrary to what Jesus and the Apostles taught. The truth was therefore neglected in mainline Christianity until Joseph Smith received his vision from the angel Moroni, and restored the original teachings of Christ and the Apostles. While similar to mainline Christian doctrine in many respects, LDS doctrine does depart significantly from a number of historically-held "Christian" views, among them the doctrine of God.
Mormonism's version of God is neither pre-existent nor omnipresent. Moreover, the Mormon version of the Trinity is markedly different from classical Nicene Trinitarianism, conceiving instead of three separate Gods literally born in different times and places from one another. This view of God is maintained across a broad spectrum of LDS source material, including Teachings of the Prophet Joseph Smith (345-349), Key to the Science of Theology by Parley P. Pratt (23), Abraham 4:1, and Apostles Orson Hyde (Journal of Discourses, 1:123) and Brigham Young (Journal of Discourses, 1:50). Thus, I think it is fair to say that the Mormon view of God is irreconcilably different from the Catholic and Protestant view of God. And I don't think that most Mormons would disagree with that assessment.
The Quran does not say, "Everything before this is crap. Here's the truth." It says, "We continue the teachings of the previous faiths, but here are a few corrections to what they believe." Again, very loose generalization intended to give the big picture that Islam, as defined in Islam, is a continuation of Judaism and Christianity. It doesn't adopt everything 100% from those religions, but it is a continuation.
Thus, to say that the Judeo-Christian God is not the God of Islam is actually in opposition to the central teaching of Islam.
It's not quite that simple, though. Islam does not teach that Christians, Jews, and Muslims all worship the same God. Rather, it holds that Allah is the only true and living God to which the Jewish and Christian Scriptures originally testified. However, those Scriptures have become corrupted over time and therefore by the time of Muhammad were no longer to be considered completely reliable. Just as Joseph Smith's angelic vision is held by Mormons to signal the restoration of doctrinal truth, so also Muhammad's angelic vision is held by Muslims to signal the restoration of doctrinal truth. This is the Islamic doctrine of abrogation: where the Old and New Testaments err, the Qu'ran and Hadith correct them--and one of the most egregious errors in Jewish and Christian Scripture, according to Islamic teaching, is the departure from belief in Allah and the concomitant advocacy of false gods (Yahweh/Jehovah, Jesus, the Holy Spirit, etc.). The only way that Jews or Christians may come to worship the true God to whom their Scriptures originally pointed, is by converting to Islam. That's why the Islamic version of hell contains two levels reserved for the everlasting punishment of Jews and Christians (Al-Hut?amah and Laz?a respectively; cf. Dictionary of Islam, edited by Thomas Patrick Hughes [Clifton: Reference Book Pub., 1965], 171.)