Bullsh — at NO point has the Christian church said Allah is the same as God. Read it carefully and it says that “together with them we worship one God” — it acknowledges that Moslems are monotheists. It does NOT acknowledge that they worship the SAME god.
841 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 they adore the one, merciful God, mankind's judge on the last day."
Near as I can tell, the mohammedans assert that God is One, that He is merciful, and that He will judge mankind.
If so, they are correct in so asserting. That may well be the extent of their correctness ... and what I have seen suggests that they go off the rails pretty quickly after that. Still ... it puts them ahead of Marxist Communists, for example, who deny God entirely.
I will let my answer to ArrogantBustard (to which you have already been pinged) supply my exhaustive reply, but in summary, Allah cannot be the God of Abraham.