Muslims do acknowledge the one God, even if they profess other errors. First, I think there should be noted the difference between worshiping God in Spirit and in truth, offering Him “true worship,” having supernatural faith, obeying Him, etc., and acknowledging God or worshiping God according to religion (which is not a theological virtue; it falls under natural justice).
St. Thomas defines this virtue in the Summa as “to show reverence to one God under one aspect, namely, as the first principle of the creation and government of things.”
SUMMA THEOLOGIAE: Religion (Secunda Secundae Partis, Q. 81)
Muslims certainly worship God as First Principle and Supreme Governor of all things, but is it the same God we know? Can one acknowledge the one God without acknowledging the Trinity?
Faith is required to acknowledge the Trinity. The Trinity cannot be reasoned out, as St. Thomas explains:
I answer that, It is impossible to attain to the knowledge of the Trinity by natural reason. For, as above explained (12, 4, 12), man cannot obtain the knowledge of God by natural reason except from creatures. Now creatures lead us to the knowledge of God, as effects do to their cause. Accordingly, by natural reason we can know of God that only which of necessity belongs to Him as the principle of things, and we have cited this fundamental principle in treating of God as above (Question 12, Article 12). Now, the creative power of God is common to the whole Trinity; and hence it belongs to the unity of the essence, and not to the distinction of the persons. Therefore, by natural reason we can know what belongs to the unity of the essence, but not what belongs to the distinction of the persons.
newadvent.org/summa/1032.htm
Therefore, we can know of God, as the Principle of all things, apart from faith, but we can only know of the Trinity with faith since it is a revealed dogma. The First Vatican Council also defined that God can be known from natural reason alone (Dei Filius, Canon 2.1) and St. Paul says, on account of this, those who do not acknowledge God (but worship idols, are atheists, etc.) are without excuse (Rom. 1:20).
Therefore, one can acknowledge the one God and Creator of all things without having faith and acknowledging the Trinity.
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