A most interesting thread. Well, really two threads. I can't figure out if it is about the Catholic Church or the religion of Islam!!
Since I can't fuse the two together, I will just comment on a personal experience with Islam.
Two years ago, when I was taking World Religions for my Seminary degree, we chose to go to a Mosque. The Imam was from Egypt, had memorized the Qur'an and had a degree in comparative religions, and he knew the Bible better than most lay Christians. He tried to convert our class, of course, but didn't have a lot of luck.
I found the people to be kind and friendly, and spent a lot of time talking with them. However, the thing I really walked away with, is the the Muslims believe in the Torah - The first 5 books of our Bible. I found that interesting, because if you read it, it really is the story of the Jews, with a few verses about Ishmael. So why they feel it is true, when it is not really about them, I do not know.
The other thing the Imam said was although they believe in the gospels, BUT the 4 "gospels" and the rest of the New Testament have been "corrupted". That gives them a lot of wiggle room to deny everything the Bible says about Jesus, except that he is a prophet, and Messiah, who is coming at the end of the age. I found that interesting, but even when our prof challenged the Imam about was it "possible" that God could come down as a man to earth from heaven, the Imam said he could, but he wouldn't. End of conversation.
So that tells me that the Muslim religion does not believe in the revelation of Jesus Christ as God and man.
So whatever else the Catholics believe, they do believe in the divinity and humanity of Christ. The Muslims do not. So regardless of what the Pope says, it cannot be the same religion.
Of course, I am neither Catholic nor Muslim, just relating my own experiences I garnered at the Mosque.