How can billions of people be condemned just because of where they were born?

Question:  You are a Christian, and therefore saved, because you happen to be born in a family that's Christian, in an area where Christianity is prominent. If you had been born in, say, India, you'd be Hindu.  If you were born in China, you'd probably be Buddhist. How can someone be condemned because he had the bad luck of being born in a non-Christian country?  Billions of people--billions!--have simply had the misfortune of being born in a world where they never heard of Jesus.  So they're going to hell, basically, because of geography--for having the bad luck of being born in the jungles of Borneo.

Response:  Firstly, no one is "saved" simply because he's a Christian.  (The implication in the question above is that you will definitely go to heaven simply because you accepted Jesus into your heart).  That's an objection that can be posed to fundamentalist Christians, but it's not what Catholics professes.  

Secondly, no Hindu, Buddhist, non-Christian is "condemned" (that is, going to hell) simply because he never heard of Jesus.

Jesus tells us quite plainly in Scripture that “If I had not come and spoken to them, they would not have sin; but now they have no excuse for their sin”--John 15:22.  That is, those who have never heard of Christ "would not have sin" and are therefore not condemned.

A document from Vatican II, Lumen Gentium professes: Those also can attain to everlasting salvation who through no fault of their own do not know the gospel of Christ or his Church, yet sincerely seek God and, moved by grace, strive by their deeds to do his will as it is known to them through the dictates of conscience. Nor does divine Providence deny the help necessary for salvation to those who, without blame on their part, have not yet arrived at an explicit knowledge of God, but who strive to live a good life, thanks to his grace" (Lumen Gentium, no. 16).

Our Catechism proclaims:  The Catholic Church recognizes in other religions that search, among shadows and images, for the God who is unknown yet near since he gives life and breath and all things and wants all men to be saved. Thus, the Church considers all goodness and truth found in these religions as "a preparation for the Gospel and given by him who enlightens all men that they may at length have life." (CCC 843)

So this then prompts 3 questions:  

1) Why even evangelize if non-Christians are going to heaven too? 

2) Doesn't the belief that non Christians are going to heaven contradict the Bible which states that no one gets to heaven except through Jesus--"no one comes to the Father but through me"--John 14:6

3) Doesn't this belief contradict the Catholic Church's own teaching which is:  "Outside the Church there is no salvation"?

Response to #1:  the question overstates the Church's teaching.  We don't profess that non-Christians ARE going to heaven.  Only that they MAY be able to.  Their "best shot" at standing before the Eternal Throne of heaven is...by embracing Christ and His Church, which is why we always want to share the good news with others.

An (imperfect) analogy is this:  we need to cross a raging river.  Catholics are in a boat.  Non-Catholics may be able to cross the river, but it really would help them if we invite them in to our boat.  It's a special kind of mean to look at them, floundering in the river and say, "Hey, I understand that you may be able to get to the other side, so...good luck to you!  Buh-bye!" 

In other words:  all of us need the Eucharist!  All of us need the grace conferred by the sacraments to eschew sin and embrace the Light.  All of us need the mystical body of Christ, the Catholic Church.

Questions 2 and 3 will be addressed at a later date!