A "Christian" is defined thusly: A believer in Jesus Christ as savior: somebody who believes that Jesus Christ was sent to the world by God to save humanity, and who tries to follow his teachings and example".
Per that "Lumen Gentium" you cited, The Pope disagrees with the words of Jesus Christ that HE (Christ) is the one route to salvation. How can one disavow Christ's teachings on salvation and define oneself as "CHRISTian"? How can one praise those who worship other "gods" for their worship of that "god"; (as done is topic 16 of the Lumen Gentium) and the islamic "god" IS another "god"; and equate that worship of another "god" with the worship of the Christian God and still be a CHRISTian?
Their "god" didn't have a son. Our's did. So much for the "same god" idea*. Either Our God was lying to them about that, another being was lying to them professing to be "God" (large "G") and they bought into it, or they are lying about their god being OUR God. Take yer pick.
*http://answering-islam.org.uk/Silas/son2.htm
excellent post dzzz
I'm on the books as Catholic but I go to Calvary Chapel because I don't agree with some of the Catholic doctrines. As far as the infallible Pope goes, Peter was the first "Pope" and he made a mistake that Paul corrected him on big time. So although I believe there are MANY saved legitimate Christians in the Catholic church, and I defend her often, I think they need to work on a few things doctrinally.
It looks like the Pope sees the road to Christ as beginning in morality and a belief in a creator. The intent seems to be that, with the Pope's blessings, and with the picture, however distorted, that they have of God, some of these Muslims sooner or later would come to believe in Jesus Christ, in the next world if not this one (i.e. in a purgatory). It actually isn't too far from some of C. S. Lewis's speculations about conversions that take place "under the cloud." Now whether this is credible is another story. The way many (not all) Muslims carry on seems to imply that they have cast the devil as their god.