This question is about what Muslims believe about this question. It isn’t a question about what it says in the Catechism of the Catholic Church about it.
You may find a few muslims who are brand new to the faith that believe that. However, a muslim who’s spent any significant amount of time reading the Qur’an will see its numerous rebukes towards trinitarian christians, especially as it pertains to the humanity of Jesus Christ [peace be upon him].
Since catholics are trinitarians and muslims are unitarians, it would be impossible for a knowledgeable muslim to believe that muslims and catholics worship the same God.
Hmm. Well historically, both religions worship the God of Abraham, Ishmael, Moses, etc…? In that respect they are referring to and worshiping the same God. But they do have different ideas about that God, and so when it comes to those ideas, there are differences? Suppose we both believe there is currently a president of the USA, but none of us has ever seen him. One believes he is white, another believes he is black. Do we believe in the same person, although we have different ideas about his attributes?
They are monotheistic–in that they believe in one God. They believe in Jesus–but as a prophet only. Also, I believe they are certain that both God and Jesus carry rocket launchers to deal with every other faith but Islam as we are all infidels to them!
Rocket launchers are overrated. I’m more of a rocket lawn-chair fan. I like to sit back, relax and ascend to higher knowledge. It’s comparable to someone who’s sitting in a lawn-chair, sipping iced tea and is propelled upwards by rockets.