In traditional Catholic teaching and philosophy the true God can be discovered by natural means without access to revelation. He is the non-contingent Creator. By it’s very essence, such a being must exist and can only be one. Therefore any person or people who believed in and adore such a non-contingent being and Creator on which all else is contingent have always been deemed to have discovered the true God. Divine revelation is needed to know of the persons of God and other truths about Him, but knowledge of them is not necessary to have knowledge of God.
No one would argue that Jews worship a different God. Likewise, St. Paul says that the pagans in Acts 17:23 are also worshiping the same God even though they do not yet acknowledge the Trinity (in the same chapter he also cites pagan poets teaching about the true God).
Acts 17:23 For passing by, and seeing your idols, I found an altar also, on which was written: To the unknown God. What therefore you worship, without knowing it, that I preach to you:
Muslims may believe falsely alledged revelations about Him, but they definitely acknowledge Him. They do not seek to worship the creature rather than the Creator as idolotors and polytheists do (who often worship beings that do not exist, but which have a contingent essence). Here are some more examples demonstrating Catholic thought on this:
St. John Damascene in his "Founts of Knowledge"
These used to be idolaters and worshiped the morning star and Aphrodite, whom in their own language they called Khabár, which means great. And so down to the time of Heraclius they were very great idolaters. From that time to the present a false prophet named Mohammed has appeared in their midst. This man, after having chanced upon the Old and New Testaments and likewise, it seems, having conversed with an Arian monk, devised his own heresy…He says that there is one God, creator of all things…
(notice, they are no longer idolators but are considered heretics)
Pope St. Gregory VII (11th century) to a Muslim prince: ‘Almighty God, who wishes that all should be saved and none lost, approves nothing in so much as that after loving Him one should love his fellow man, and that one should not do to others, what one does not want done to oneself. You and we owe this charity to ourselves especially because we believe in and confess one God, admittedly, in a different way, and daily praise and venerate him, the creator of the world and ruler of this world.’
The famous counter-reformation Jesuit and expert on St. Thomas Aquinas, Suarez:
Thomas, however, rightly distinguishes two kinds of religious practices: there are those which go against reason and against God insofar as he can be recognized through nature and through the natural powers of the soul, e.g., the worship of idols, etc. Others are contrary to the Christian religion and to its commands not because they are evil in themselves or contrary to reason as, for example, the practices of Jews and even many of the customs of Mohammedans and such unbelievers who believe in one true God.
Suarez, Tract. de Fide Disp. 18 Sect. III
(Notice, the worship of idols is intrinsically evil because it goes against reason (the true God can be known by natural reason), yet many practices of the Muslims are not intrinsically evil in and of themselves since they are reasonable acts of worship directed to the one God.)
Catechism of Pope St. Pius X : 12
Q. Who are infidels?
A. Infidels are those who have not been baptised and do not believe in Jesus Christ, because they either believe in and worship false gods as idolaters do, or though admitting one true God, they do not believe in the Messiah, neither as already come in the Person of Jesus Christ, nor as to come; for instance, Mohammedans and the like.
(again, they are not idolators but are like Jews)
Catholic Encyclopedia: As in ecclesiastical language those who by baptism have received faith in
Jesus Christ and have pledged Him their fidelity and called the faithful, so the name
infidel is given to those who have not been baptized. The term applies not only to all who are ignorant of the
true God, such as pagans of various kinds, but also to those who adore Him but do not recognize
Jesus Christ, as Jews and
Mohammedans.
Second Vatican Council: The Church regards with esteem also the Moslems. They adore the one God, living and subsisting in Himself; merciful and all- powerful, the Creator of heaven and earth, who has spoken to men; they take pains to submit wholeheartedly to even His inscrutable decrees, just as Abraham, with whom the faith of Islam takes pleasure in linking itself, submitted to God.
See also this chapter on Islam in
Hillair Belloc’s "Great Heresies."
ewtn.com/library/HOMELIBR/HERESY4.TXT
Muslims, like the pagans St. Paul met, worship the true God without knowing it, even though they have been misled as to truths about him by a false prophet.
(of course, a Muslim in good faith and good will who desires to solely humble and abandon himself to the way, truth, and life of God for love of God alone, implicitly desires Christ who is the way, the truth, and the life and
may be saved. However, one who simply adores the one God while obstinately rejecting the Son of God–the way, the truth, and the life–has neither the Father nor the Son and cannot be saved.).
Catholics and Muslims do indeed worship the same God. There is only one God.