I am a recent Catholic convert (it has been 1 year as of Oct. 4). I came from a Calvinist background (the PCA denomination). Several months ago I started an apologetics Bible Study in my parish. During one of our initial meetings I was stunned to hear parishoners express the belief that all good people, regardless of their religious beliefs, go to heaven. This was regardless of whether one was a follower of Moses (Judiasm), Allah (Islam), Buddah or some other faith. I further discovered that a number of American Bishops stated we should not evangelize the Jews, implying that Judiasm is a valid and sufficient path to God.
In looking into the matter I thankfully came across a document called DOMINUS IESUS. I encourage every Catholic to get the document off the web, read it and believe it (I think I got mine from the Vatican website). I would especially point to section VI. THE CHURCH AND THE OTHER RELIGIONS IN RELATION TO SALVATION.
Some quotes (random):
This truth of faith does not lessen the sincere respect the Church has for the religions of the world, but at the same time, it rules out, in a radical way, that mentality of indifferentism characterized by a religious relativism which leads to the belief that ‘one religion is as good as another’.
If it is true that the followers of other religions can received divine grace, it is also true that objectively speaking they are in a gravely deficient situation in comparison with those who in the Church have the fullness of the means of salvation"
With respect to the way in which the salvific grace of God - which is always given by means of Christ in the Spirit and has a mysterious relationship to the Church - comes to individual non-Christians, the Second Vatican Council limited itself to the statement that God bestows it “in ways known to himself”.
…it cannot be overlooked that other rituals, insofar as they depend on superstitions or other errors (cf. 1 Cor. 10:20-21), constitute an obstacle to salvation.
…it is clear that it would be contrary to the faith to consider the Church one way of salvation alongside those constituted by the other religions, seen as complementary to the Church or substantially equivalent to her…
Equality, which is a presupposition of inter-religious dialogue, refers to the equal personal diginity of the parties in dialogue, not to doctrinal content…
[End of quotes]
In summary, it is possible for non-Christians “in ways known to God himself” to be saved. But at the same time it is recognized that followers of other religions are in a “gravely deficient situation”. In other words, there is still an urgency for the Great Commission as these people need to be rescued their “grave situation” where they are embracing a false way of salvation.
I hope this helps to clarify (oh for clarity in the teaching of the Church!) our Catholic beliefs of the non-Christians need for Christ.