It is impossible IMO, to hold that Christians have the same God as Muslims or Jews. The consistent mentioning of this acceptance of monotheism somehow = the one true God after the explicit revelation of Christ to the world I think is a total contradiction because what I don’t hear in these analogies is the difference between an unknowing with a certain confusion due to the time in salvation history someone is living in or maybe a culture that comes to believe in one God through natural theology vs an explicit rejection of Christ therefore God. If the point is do they worship one God then okay, sure; but to say they worship our God? The Trinity in some confused way? While also rejecting Christ? This is not possible!
Within this discussion the idea often comes up that “well did Moses understand the Trinity?” as a defense of this position. We don’t know if he had a conception of Trinity in his earthly life so at best, we have an argument from silence or just no verdict but at the Transfiguration it is somewhat clear Moses endorses Christ. Again, not knowing clearly vs rejecting are totally different things. Christ's own words deny the multiple road pathway to God.
• John 14:6 Jesus saith to him: I am the way, and the truth, and the life. No man cometh to the Father, but by me.
• John 5:23 That all men may honour the Son, as they honour the Father. He who honoureth not the Son, honoureth not the Father, who hath sent him.
• 1 Timothy 2:5 For there is one God, and one mediator of God and men, the man Christ Jesus.
How can we possibly say we worship the same God as them when ours has made this impossible? Again, if we want to say monotheism, sure. To say they can worship the same God with us without the Trinity and Christ post revelation is simply false. My question to that would be what would it take besides a monotheistic belief to rationalize that a different group worships the same God as us? Or better framed, how much of the revelation we possess can someone reject yet still be right?
Muslims do not believe they worship the same God as us which just adds to the case that this position is untenable. Islam’s Quran opposes those “who say that God is the third of three” (5:73). A further passage declares that “we worship God alone; we ascribe no partner to Him, and none of us takes others beside God as lords” (3:64; similarly in 6:161-163). The Quran also says that God asked Jesus, “Did you say to people take me and my mother as two gods alongside God?” Jesus then denied this (5:116).
The Angelic Doctor has a great quote that I have seen, which I am sure many are familiar with, “On the contrary, he [Muhammad] perverts almost all the testimonies of the Old and New Testaments by making them into fabrications of his own, as can be seen by anyone who examines his law. It was, therefore, a shrewd decision on his part to forbid his followers to read the Old and New Testaments, lest these books convict him of falsity. It is thus clear that those who place any faith in his words believe foolishly.”
If we want to reject Christ’s teachings, Islam’s own teachings, Jewish beliefs, Aquinas and just basic common sense about the laws of non-contradiction and the impossibility of rejecting such a fundamental component of something while also claiming to accept it, then sure I guess you can say we worship the same God as Muslims and Jews. I reject that position as they reject Christ as Lord and God.