This paper at the EMFJ site sets forth the theory that the "Great Architect of the Universe" (G.A.O.T.U.) is a cover name, used in order to make it possible for people of different religions to pray together. This is partially correct. But before we draw conclusions or pass judgements, we should examine the matter of Christians vs pagan worship.
Christianity arose in a polytheistic world where it was considered normal to worship several gods. Many of those who were interested in becoming Christians did not realize that this meant giving up all other religious activities and associations. Indeed, this is still a problem for missionaries in polytheistic cultures; the imperative "You shall have no other gods beside me" seems unreasonable to polytheists. They want to worship Christ, but do not understand the Christian claim to exclusivity; there are no other gods!
This made it necessary for the Apostles to set up rules for worship and behavior versus the surrounding, pagan culture. Converted pagans would ask "Can I still visit my old temple?" or "Can I eat sacrificial meat?". (It was normal that all animal slaughter was performed as sacrifices to some deity.) The answers in the New Testament are clear. Worship is not only something you do in your heart, but also a statement of your faith to the world. 1 Corinthians 10 explains it:
The point is that Christians should make it clear that they never pray to anyone or anything except the one true and living God who the New Testament tells us about. In the context of the Masonic lodge, there is no risk for such misunderstanding. You are free to tell others that you are a Christian, and that G.A.O.T.U. for you means God the Holy Trinity. Everyone knows this. Even if the person next to you has a false and idolatrous faith, it is quite clear that you are not praying to his god or demons. Indeed, you have no guarantee that everyone is praying to the true God even in church! They guy next to you may secretly be a satanist... You can not know, and you need not concern yourself because God knows all secrets.
The term "G.A.O.T.U." for God is not a Masonic invention. Jean Calvin (1509-64, one of the originators of the modern Evangelical tradition) repeatedly calls God the Architect of the Universe in his book "Institutes of the Christian Religion". It is doctrinally correct for a Christian, since God is indeed the Creator and it says nothing false about God. Freemasonry also has other words for God. In the First Degree prayer, he is called "Almighty Father and Supreme Governor if the Universe". In the Second, "Merciful Lord", and in the Third degree, "Almighty and Eternal God, Architect and Ruler of the Universe". These descriptive vocatives are compatible with all monotheistic religions, since they do not mention any of the things that set their faiths apart. Using them does not implicate that you are worshiping any other god than the same one you pray to in church.
In the 17th century, a syncretistic movement arose which is known as "Deism". Deism became popular among radicals in the 18th century, and it was the official "religion" of the French Revolution. It states that all religions actually worship the same god, simply using a variety of different names for him. As a consequence, all religions are equally valid, equally true, and equally good ways to salvation. The deists appropriated the term "G.A.O.T.U." to describe God, since it only says that there is a god who has created the universe. The term in itself is not a name but a description.
But it is a widely spread misunderstanding that Freemasonry is deistic. It is not.
Freemasonry does not propagate the ideas of Deism. EMFJ tries to prove that Masonry is deistic by quoting from Christopher Haffner's book "Workman Unashamed", where he asserts that in his personal belief, Moslems and Hindus in the lodge "are praying to the same God as I, yet their understanding of His nature is partly incomplete (as indeed is mine...)". This is a testimony from one Christian Freemason, not an official declaration of Masonic doctrine. Myself and many others believe that Haffner is wrong. A Hindu who prays to Shiva is not praying to the same god that Christians worship.
The British-American type of Freemasonry admonishes all Masons to be diligent in their own religions. It makes no statements on whether these religions are equal or true. It does not propagate any form of syncretism, and neither affirms or denies the teachings of any religion. It does not claim that different religions are actually worshipping the same god. Freemasonry makes only one religious statement: that there is a God who created the Universe. In this, it draws a line between religious believers and godless people. It does not concern itself with the lines between religions, because it is itself not a religion, and the various temples and churches are better equipped to define the various eternal verities.
Freemasonry happens to profess one truth which is common to all major religions. EMFJ portray this as syncretism. That is like saying that Christians should not believe in the theory of relativity because Einstein was a Jew, or that we should not believe that God is almighty because the Moslems do. This is bigoted and false. Imagine that you are standing in the street, and suddenly you see the mushroom cloud of an atomic bomb going off a few miles away. You face immediate death. You kneel down in prayer, putting your soul in the hands of God. Does it bother you that a Hindu and a Moslem are doing the same thing a few feet away? If you are that bigoted, you should not become a Freemason. If you are a true Christian, you should pray for the Jews and the Moslems, and win them over by showing them the love of Christ.