It doesn't matter how other religions define God. He is Who He is as He doesn't change.
God either is Who He says He is or He isn't. Others do not get to define Who He is. He has defined Himself.
Both Jews and Moslems profess to worship and adore the God of Abraham, Isaac, and Jacob in their own respective languages, as do you.
Well, if the CCC had put it that way you might have an argument.
However CCC 841 doesn't put it that way.
The Church's relationship with the Muslims. "The plan of salvation also includes those who acknowledge the Creator, in the first place amongst whom are the Muslims; these profess to hold the faith of Abraham, and together with us(catholics italics and insert mine) they adore the one, merciful God, mankind's judge on the last day."330
The only way to read this is the ccc is pointing to one God.
You can point to different renderings all you want.
The question remains....is God the same in the OT and the NT?
Catholics have boxed themselves in on this way as seen by catholic attempts to parse words like the Clintons.
To rwa265's point....He is not the same God as worshipped by the Muslims. To continue to insist He is shows a complete lack of understanding of just Who God is as He has revealed Himself in His Word.
When catholics say Jews reject Messiah, that is bias on their part as not all Jews have rejected Messiah. There are a lot of catholics who have rejected Messiah as well by their allegiance to Mary. There are a lot of Gentiles who have rejected Messiah as well.
We're still left not knowing for sure who it is catholics and muslims worship/adore.
The bottom line is, continues to be and always will be.....God is the same in the OT and NT and HE DOES NOT CHANGE.