There is a great deal of confusion in the Church today as to whether or not Muslims worship the same God as do we. In fact many prelates, including our own Cardinal McCarrick, either are honestly confused about the matter or they exploit general confusion so that they may appear to be "ecumenical". Indeed, nine years ago at Catholic University His Eminence addressed some Muslim dignitaries; in that address he invoked "allah" three times but he gave not one mention to Jesus Christ. That address, which can be called de facto idolatry, is here.
Cardinal McCarrick and other devotees of ecumenicide often cite Lumen Gentium and the Catechism as their authorities. They are misreading those church documents. A few weeks ago Dr. Taylor Marshall posted an article that addressed this question. I link to it now; it's worth careful study. He points out that the Church documents state that the Muslims profess to worship the God of Abraham, and profess to hold faith in Him.
It's one thing to profess to worship God. It can be quite another to worship God in fact. Here's an example of this occurrence. We've all heard Nancy Pelosi's protestations of being a "good faithful Catholic". This is the same Pelosi who went on a rampage when her bishop upheld traditional marriage. This is the same Pelosi who was honored at Planned Parenthood's gala in March and said that" to be associated with the great Margaret Sanger is a distinct privilege" (she may well "enjoy that privilege" for all eternity if she doesn't repent, but I digress). She also believes Hamas to be a "humanitarian organization". So Pelosi may think she's a great Catholic, but reality indicates otherwise. Similarly, Muslims think they worship the God of Abraham but their actions indicate otherwise. The more vociferous Muslims state that we don't worship the same deity (more than we can say for Cardinal McCarrick); they just don't accept that they are the ones worshiping a false idol - if not actual demons.
Below is a video of Muslim jihadists burying alive opponents. This action (among so many others) is evidence that these monsters do NOT worship the One True God. Parents - you may wish to keep your small children from seeing this.