Catholics will need to answer that for themselves. From the Catechism of the Catholic Church:
841 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."
Sorry, Alex: Muslims adore a horrendously distorted notion and tragically incomplete vision of the one, true God. But contrary to claims that “Allah” is some sort of a moon God, it is a semitic word that has meant “god/God” since long before Mohammed came along. Yes, one can use “allah” to refer to a pagan god, just like I just used the word “god” to refer to a pagan god. But the Moon god of Mecca was Sin/Suen, and those pagans of Mecca were not monotheistic, so using “allah” to refer to Sin/Suen outside of Ur or Harran would be contextually improper.
“Why did Mohammed presume that the Arabs already knew who Allah was?”
Had Allah meant Sin/Suen, Mohammed would’ve had to suggest to those outside the Cult of Sin that Allah meant Sin, specifically, especially given that Allah is described in so many ways that contradict the depiction of Sin. But since “Allah” meant “the God,” all Mohammed needed to do was to assert the nature of God. OF COURSE, MOHAMMED’S DESCRIPTION OF GOD IS CONTRARY TO CHRISTIANITY. The same catechism from which paragraph 841 is taken contains many condemnations and descriptions of what it labels “indifferentism,” the notion that it doesn’t matter what doctrine one holds or what sect one belongs to.
Contrary to the common assertion that the Koran doesn’t explain who Allah is, he is repeatedly referred to as “the god of Abraham,” “the god of Mose,” “the god of the Christians,” and so forth.
Names of Allah in the Koran:
“Lord of Heaven and of Earth, God of Mercy”
“God of Mercy” (more than 50 times)
“God of Moses”
“God of the entire universe”
“God of all in Heaven on on Earth”
“God, Lord of the Heavens of Lord of the Earth”
Refutations of Sin from within the Koran:
“There is no God but me.”
“Your God is the one god.”
“Abraham was a leader in religion, obedient only to Allah”
“Thou follow the religion of Abraham, the sound in faith”
(Obviously Muslims believe incorrectly in what the religion of Abraham was, but plainly it was not that of the Moon God.)
“To you he has commanded the faith, which he gave to Noah, which we (the angels) have revealed to thee, and given commands to Abraham, and Moses, and Jesus.”
(Again, there heresy here is obvious; the point is that it is ridiculous to suggest that the Arabs believed Jesus worshipped the moon god.)
Catholics will need to answer that for themselves.
Catholics neither propose nor need to answer that question.
As shown in the quote you posted from the Catechism, the only question we propose to answer is that they (1) profess to worship the God of Abraham and (2) do indeed worship the one, true God. From that point on, great saints such as JPII have said such as the following:
Whoever knows the Old and New Testaments, and then reads the Koran, clearly sees the process by which it completely reduces Divine Revelation. It is impossible not to note the movement away from what God said about Himself, first in the Old Testament through the Prophets, and then finally in the New Testament through His Son. In Islam all the richness of God's self-revelation, which constitutes the heritage of the Old and New Testaments, has definitely been set aside. Some of the most beautiful names in the human language are given to the God of the Koran, but He is ultimately a God outside of the World, a God who is only Majesty, never Emmanuel, God-with-us. Islam is not a religion of redemption. There is no room for the Cross and the Resurrection(p. 92).
Eagleone posted a helpful link on this same issue before and I'll post it here for anyone who is interested in the Catholic view on this issue:
http://www.catholic.com/blog/tim-staples/do-muslims-worship-the-same-god-catholics-do
An excerpt:
Thus, we Catholics have to be careful to distinguish between the fact that Muslims believe in the one true God “living and subsisting in Himself; merciful and all-powerful, the Creator of heaven and earth,” and the fact that they get it wrong—profoundly wrong—when it comes to both who God has revealed himself to be in the New Testament, and what he has taught his people.