Avery Cardinal Dulles, after surveying Roman Catholic teaching through the ages about who can be saved gives this bottom line answer:
Who, then, can be saved? Catholics can be saved if they believe the Word of God as taught by the Church and if they obey the commandments. Other Christians can be saved if they submit their lives to Christ and join the community where they think he wills to be found. Jews can be saved if they look forward in hope to the Messiah and try to ascertain whether God’s promise has been fulfilled. Adherents of other religions can be saved if, with the help of grace, they sincerely seek God and strive to do his will. Even atheists can be saved if they worship God under some other name and place their lives at the service of truth and justice. God’s saving grace, channeled through Christ the one Mediator, leaves no one unassisted. But that same grace brings obligations to all who receive it. They must not receive the grace of God in vain. Much will be demanded of those to whom much is given.
So if Catholicism is correct, I guess most of us in other churches are OK. I worry that the atheists will be unhappy to find themselves in Heaven, irked that in not believing in God they nevertheless worshiped him under some other name, so what kind of Heaven would that be for them?
But let me get this straight, and keep in mind that Cardinal Dulles is no touchy-feely Catholic but a conservative Catholic in close association with the Pope. To be saved, you do not have to have faith in Jesus Christ. You can have faith in God. Or, despite the first commandment, you can have faith in God under some other name. Or, if you don’t believe in any gods, you can have faith in something else, such as truth or justice. Or, if you don’t have faith in anything, you can be saved by your good works, though this seems to be the main point even for Christians.
Certainly, if salvation is by good works, anyone who does good works–people of other religions, atheists–will be saved. And since Catholics define good works as having been produced by faith, one can predicate some sort of efficacious faith to anyone who does them. But what an impoverished view of sin we see here! So even this blatantly human rationalization to make God seem nice turns out to be of little comfort to an actual sinner who is burdened by his bad works.
But more than that, if faith in virtually anything is enough or even optional for salvation, why do we need the church, why should anyone evangelize, and why did Jesus need to die?