The reason is that the question of “do Christians and Muslims worship the same God of Abraham?” is not a theological question as such. It may seem to be that way, but it is not. It is merely a question of fact.
Sometimes questions address an issue that is so fundamental or foundational that the question does not rise to a level where any person with both a basic knowledge of the religion and logical thinking will necessarily accept the answer as a “given.”
No one (no one with basic knowledge and logical thinking) would say that Catholics and Lutherans worship different Gods. No theologian would even consider that to be a legitimate question. A simple “yes they do” suffices; or at least, should.
Now, fanatics on either side might present their cases. One says “the Catholic God told the popes to sell indulgences therefore we believe in a different God.” Another says “Luther’s God told him to take books out of the Bible, therefore we believe in different Gods.”
Statements like that, reasoning like that, is immediately dismissed off-hand. It does not rise to the level of being something debatable.
Same thing applies here. The question “what God do Muslims worship?” is not a complicated question. It requires only a basic understanding of Christianity and Islam to know immediately that the 2 religions worship the same One God, albeit in different ways, and saying different things about that One God.
Someone can say “Islam says different things about God” all day long. That won’t change the fact that the God they claim is identified as the God of Abraham. This is true because such thinking immediately changes the question from “what God?” to “what do they say about God?”
As far as the Catholic Church is concerned, this question is not one that is debatable. Not because it has been defined as a dogma or doctrine, but because it is a known fact.
I can go on all day providing examples of the fact that the Catholic Church knows and does not hesitate to affirm that Christians and Muslims worship the same God of Abraham. How many such examples should be necessary to prove that basic point? The Church accepts this as a given.
The debate part comes later. What that exactly that means going forward into the details of Christian-Muslim relations is the part that is open to debate and discussion.