The teaching of the church is very vague on this topic. By saying that Muslims claim to be worshipping the God of Abraham, and not following it up with any reference to Christ being a part of God, is not doing justice to one's beliefs.
If that is true, then we worship the same God.
If we worship the same God, then Muslims are Christians. I am sure that you would agree with that statement. Do you?
In spite of our discussion, I feel adamant that unless the Catholic Church believes that Muslims are Christians, then they should not allow them to profess the God of Abraham in public. A non-christian cannot evangelize for Christ or spread the Gospel of Jesus Christ.
I can't say I do, which is why I kept alluding to the Jews. I don't define "Christian" as one who worships the God of Abraham. I define it as one who follows the teachings of Christ. Now, Christians certainly worship the God of Abraham - however, I believe that the Jews worship Him as well, despite the fact they may not know Him as He has revealed himself to the rest of us.
In spite of our discussion, I feel adamant that unless the Catholic Church believes that Muslims are Christians, then they should not allow them to profess the God of Abraham in public. A non-christian cannot evangelize for Christ or spread the Gospel of Jesus Christ.
Again, maybe you are correct; however, that same reasoning would apply to the Jews, and we would have to say the Jews don't worship the God of Abraham, the father of Israel. A tenuous position, in my opinion.
I don't believe the Church should be in the business of judging what is truly in another's heart. The way I see this is told well - much better than I could do - by C.S. Lewis in The Last Battle. The Calormene Soldier who sought Truth and the Good, despite outwardly serving Tash, was in fact serving Aslan, as He is the source of all Good.