The short answer is yes. Non-Catholics and non-Christians can be saved.
The Catechism of the Catholic Church sums it up this way:
1260 Every man who is ignorant of the Gospel of Christ and of his Church, but seeks the truth and does the will of God in accordance with his understanding of it, can be saved. It may be supposed that such persons would have desired Baptism explicitly if they had known its necessity.This is known as the "baptism of desire", an extra-ordinary way of salvation that occurs outside of the sacramental system. The Catechism also says:
1281 [A]ll those who, without knowing of the Church but acting under the inspiration of grace, seek God sincerely and strive to fulfill his will, can be saved even if they have not been baptized.Now I'll attempt to explain this in my own words. Catholics may correct or clarify what I am about to say, but Feeneyism (the belief that only card-carrying Catholics can be saved) will not be accepted. That is a heresy, and we don't do heresy here in the Bubble. At least not on purpose. :)
First, the foundation.
Every human soul is made for one end: Union with God for all eternity. However, as we've discussed before, union with God cannot be achieved without the grace of Christ, which was won for us on the Cross.
There is no salvation except through Christ Jesus, and it is simply impossible for anyone to get to Heaven without Him.
(That's the basic, immovable ground rule for the rest of what I have to say, so if you forget that as we go along, I will refer you back to it.)
Human beings are hardwired for God. Every man is expected in his lifetime to seek truth, and to do the will of God as best he understands it. People who daily strive to discover what is true, good and beautiful, and who risk great suffering to conform their minds, hearts and lives to God, are rightly called men of good will. During this Christmas season, we should recall the words of the angels who announced Christ's birth (correctly translated in Catholic Bibles but mistranslated in some Protestant Bibles*):
Glory to God in the highest;
and on earth peace to men of good will.
-- Luke 2:14
As we discussed recently, God gives everyone the actual grace to seek Him and to desire to do His will. An open heart will naturally search for truth, and as Jesus promised: "Ask, and it shall be given you; seek, and you shall find; knock, and it shall be opened to you." -- Matthew 7:7
Those who were raised up in the Catholic Faith have easier access to the fullness of truth than others, with a quicker route to sanctifying grace. That is a blessing beyond words. However, "to whom much is given, much will be required". Those who know more will be accountable for more. To know God's will and yet neglect our duties as Catholics is to act in bad faith, and we become men of bad will. (We should tremble at the thought!)
But non-Catholics who are sincerely ignorant of the necessity of baptism or who have never heard the Gospel are not responsible for the things they -- through no fault of their own -- do not know. After all, God is perfect Justice. He reads each human heart and knows who is truly seeking Him (even if that person hasn't quite found Him yet), and who desires to do His will (even if that person has it wrong at the moment).
This is the soul who would without hesitation ask to be baptized if he knew that baptism was the will of God. This is the soul who might never actually hear the name of Jesus Christ on this earth, but will see Jesus upon his death and say, "It is You! You were the One I was seeking all my life!" He will know Jesus, and Jesus will know him.
So yes, non-Catholics can be saved. And when these "men of good will" reach Heaven, when they are counted among the saints, every one of them (and us) will be of one mind and heart, one big Catholic family, professing Jesus Christ as Lord of all.
*Many Protestant translations are built upon bad theology, and thus many of their Bibles read: Glory to God in the highest, and on earth peace, good will toward men. As you can see, that changes the meaning completely!