They in fact do worship the same God, since we know that the preincarnate Word is the One who revealed Himself in the old testament theophanies to the prophets and patriarchs. They simply cannot comprehend Him and the fulness of his works, and so they worship Him in darkness, never knowing what the true object of their worship is.
I think this is an excellent argument, but how does it square with your previous comment:
If you do not know God perfectly, how can you judge what level of imperfection it takes for one's worship not to be directed towards the same God? Where do you draw the line? Can you draw a line?
I thought this indicated that it was impossible for us to make proclamations, due to not knowing God perfectly and what, if any, lines to draw. But you appear to have drawn one.
I don't really see how so. I never drew any real cut off point. It is entirely possible that those who know nothing of Christ could still worship God in ignorance, but without ever being able to name Him or gain any understanding of Him. The only thing that I denied (perhaps somewhat too hastily and without enough qualification) is that pagans worship God, because in their case, they normally worship idols—deities fashioned after created things, such as the sun and the moon—although under extraordinary circumstances, pagans may come to worship some sort of transcendent or unknown deity, at which point they might be said to worship God in ignorance as well. St. Paul, being ever clever, manages to play upon this idea in his sermon upon the Areopagus.
"Then Paul stood in the midst of Mars' hill, and said, Ye men of Athens, I perceive that in all things ye are too superstitious. For as I passed by, and beheld your devotions, I found an altar with this inscription, TO THE UNKNOWN GOD. Whom therefore ye ignorantly worship, him declare I unto you. God that made the world and all things therein, seeing that he is Lord of heaven and earth, dwelleth not in temples made with hands; Neither is worshipped with men's hands, as though he needed any thing, seeing he giveth to all life, and breath, and all things; And hath made of one blood all nations of men for to dwell on all the face of the earth, and hath determined the times before appointed, and the bounds of their habitation; That they should seek the Lord, if haply they might feel after him, and find him, though he be not far from every one of us: For in him we live, and move, and have our being; as certain also of your own poets have said, For we are also his offspring. Forasmuch then as we are the offspring of God, we ought not to think that the Godhead is like unto gold, or silver, or stone, graven by art and man's device. And the times of this ignorance God winked at; but now commandeth all men every where to repent: Because he hath appointed a day, in the which he will judge the world in righteousness by that man whom he hath ordained; whereof he hath given assurance unto all men, in that he hath raised him from the dead."
Now to be clear, I'm not arguing that it is impossible to distinguish between God and idols or created things. We know clearly that sun, moon and thunder deities are not God. But in discussing Islam, Judaism and Christianity, we are dealing then with religions which recognize some supreme being (in fact, a supreme being which is associated with causing the same set of historical events) Who is not merely some idol. That is where the line gets blurry. If we say that the 'Orthodox understanding of the Trinity' (whatever that means) is the only true God, then why must we stop there? People understand the 'Orthodox understanding of the Trinity' differently. This standard is inadmissible, because then it would mean that everybody has a different God, since nobody understands God in the same way; and then, at best, only one person would worship the true God, if that many. But once we admit any shades of grey, then we have to admit for consistency that proposing any sort of cut off line is a rather unjustifiable proposition, in my honest opinion.