If you say that Catholics and Muslims do not worship the same God, then you imply multiple Gods. That violates the very concept of The One God. The best that you can do is to say that Catholics and Muslims have different understandings of the nature of God.
Wrong. There have been and are many false gods held by man. Allah is a god but not God. Big difference. Zeus was a god worshipped by ancient Greeks. He certainly is not God. Hindus have millions of gods. None being God or a God. In their hearts and minds only do they exist.
Of course it does, but which does not mean that there are not false gods, which there are, and which is why the V2 affirmation of Muslims as worshiping the same God as Catholics is perverse. The god of Islam is a distinctly different deity than that of the Bible, which Rome has chosen to affirm is that same God as that of Rome.
The Church's relationship with the Muslims. "The plan of salvation also includes those who acknowledge the Creator, in the first place amongst whom are the Muslims; these profess to hold the faith of Abraham, and together with us they adore the one, merciful God , mankind's judge on the last day." ( Lumen Gentium 16, November 21, 1964: CCC 841; Emp. mine)
Yet as Catholicism departs from Scripture in so many basic ways then to some degree it may be said to worship a false god.
The best that you can do is to say that Catholics and Muslims have different understandings of the nature of God.
Wrong. For though there be that are called gods, whether in heaven or in earth, (as there be gods many, and lords many,) (1 Corinthians 8:5)
The best that you can do is to say Rome affirmed a false god as being the true one, as V2 was a compromise document between liberals and traditional RCs, which the traditional RC sects at least recognize, if not the other errors of Rome.
Conservative Novus Ordo Catholics who object to the drastic changes call them "abuses" that result from the "misinterpretation" of Conciliar teachings. They point to many fine and orthodox statements in support of their contention. Those on the other hand who are on the forefront of the Revolution - the Liberal post-Conciliar Catholic - can justify almost anything they wish by recourse to the same documents.
"The definitive texts are for the most part compromise texts. On far too many occasions they juxtapose opposing viewpoints without establishing any genuine internal link between them. Thus every affirmation of the power of bishops is accompanied in a manner which is almost tedious by the insistence upon the authority of the Pope...
It is then the ambiguity of the Conciliar statements which allows for any interpretation one wishes. Yet despite this one, when one reads the documents as a whole, one finds there is a certain "animus" or spirit which is "offensive to pious ears". There is, as Cardinal Suenens has said, "an internal logic in Vatican II which in several cases has been grasped and acted on, showing in everyday practice the priority of life over law. The spirit behind the texts was stronger than the words themselves."[38] — VATICAN II Rama Coomaraswamy, M.D.; http://www.the-pope.com/wvat2tec.html
If you say that Catholics and Muslims do not worship the same God, then you imply multiple Gods.
There have been false “gods” since the fall. Some groups worshiped “Ba’al,” and others worshiped “Dagon.” They were just Lucifer in disguise, much like “Allah.”