It's actually pretty simple, stated right here in the Catechism of the Catholic church, which says NOTHING about it being complicated.
http://www.vatican.va/archive/ENG0015/__P29.HTM
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."330
Our Catholic friends have come a long ways in 1,000 years when they were telling the folks they would get special grace if they join the Crusades.
I guess that’s progress...sort of....almost...
A little more to it than just Muslims believing in God and going to heaven. Now for the truth.
***************
As we have seen, God introduced salvation to the world through his chosen people, the Jews. God’s revelation to the Jews found its fulfillment in Christ, the Messiah, who established the Catholic Church. The grace necessary for salvation continues to come from Christ, through his Church. Those who innocently do not know and embrace this might still attain salvation but those who knowingly and willingly choose to reject it, reject salvation on God’s terms.
The Catechism (once again quoting Lumen Gentium) summarizes all this as follows:
Basing itself on Scripture and Tradition, the Council teaches that the Church, a pilgrim now on earth, is necessary for salvation: the one Christ is the mediator and the way of salvation; he is present to us in his body which is the Church. He himself explicitly asserted the necessity of faith and baptism, and thereby affirmed at the same time the necessity of the Church which men enter through baptism as through a door. Hence they could not be saved who, knowing that the Catholic Church was founded as necessary by God through Christ, would refuse either to enter it or to remain in it. (CCC 846)
Which sends the unofficial magisterium (which sends us to the CCC to define what Rome teaches) into hyperdrive trying to explain the CCC as not meaning what it sounds like, while criticizing us for having no infallible interpreter, as if they had one for theirs.
Rome organizationally is one church with many flavors, but whose doctrinal unity is largely on paper, existing in schism with other Catholics and with many sects, which would be far more manifest if they were more committed to doctrine. Ask the sedevacantists.