Is that a trick question?
Jews do not believe in a trinitarian God
Catholics do, so…
These are just personal musings, on my part, I suppose that it comes down to how one looks at it.
Aristotle, a pagan, believed in the idea of an unmoved mover. St. Thomas Aquinas agreed with this as a characteristic of our Lord. Is it the same God? Again, it depends on how you look at it.
While we may share certain cosmological agreements, we may differ vastly on fundamental metaphysical considerations.
It is my understanding that Gen 1:26 is understood by the Jews as God administering to and delegating creation to His Angels. He creates through/with them. Even if modern Christian scholarship seeks to cast doubt on the trinitarian implications of that particular verse as well, it is still made clear in the first few verses of The Book of John, as well as in Church dogma, that nothing was created without the Word. Creation occurred through and by the Word.
Ignorance of Christ as part of God is one thing, and may result in an incomplete understanding. Rejection is another, and may lead to a different one altogether. Ultimately we are not talking about Judaism but Islam, and islam seems to take it even further. Without having to go further, based on church dogma that the Whole Trinity participated in creation, does Islam really “acknowledge the [same] Creator,” as they condemn believers of Christ (as God), by whom creation occured? Even though Muslims “profess to hold the faith of Abraham,” do they worship the same God, or a alternate image of Him? A few shared characters don’t necessarily add up to the same Being… or do they?
It is also written, “…neither doth any one know the Father, but the Son, and he to whom it shall please the Son to reveal him.” If the Son is rejected, and believers of the Son condemned, what God do those who reject the Son believe in if not the one revealed by the Son?