Answer:
Christians answer this objection in different ways, but there are some biblical non-negotiables that are clear (and going from clear to unclear, is always a good way to understand the Bible):
1) First, all have sinned (Rom 3:23). This means that all stand justly condemned no matter the state of our knowledge about Jesus or lack thereof. Before we broach the question of the fairness of a salvation offer that only makes it to a select few (IE just to the west, or to whites, etc), we have to broach the question of the fairness of the separation all people everywhere from God.
This is a separate issue. It may be that there's a cure that's available for the sicknesses of people, and there's complex questions about who has the cure, who gets the cure, is it fair that some should have it and some don't?, etc. But first we have to ask who is sick!
The Bible says everyone is morally, mortally sick. Romans 1-3 is the eloquent argument that ends with this conclusion: Rom 3:9-12 "...we have already shown that all people, whether Jews or Gentiles, are under the power of sin. As the Scriptures say, "No one is good — not even one. No one has real understanding; no one is seeking God. All have turned away from God; all have gone wrong."
So part of the answer to this question is to ask another question - are all JUSTLY condemned? Is God being unfair to say that people by their own choice, choose to sin and reject him and must suffer the consequences? Is the default position of the human race one of being automatically saved unless they do something extraordinarily bad, or is the default position of the human race one of being separated from God (both here and hereafter) unless something extraordinarily good happens?
The Bible says clearly it's the latter. Jesus said, "...no one is good, except God" (Mt 19:17). It doesn't mean humans are not capable of doing any good, it just means that fundamentally we are broken, and often we've grown so numb we don't even see it, Eph 4:18 (which is further evidence of our brokenness!) And if God can't stand to look on evil (Hab 1:13) it stands to reason that those who are "not good" cannot enjoy relationship with an all good God. They must, by their very nature, be shut off from that which is their opposite (2 Thes 1:9).
That's the bad news as the Bible teaches it and Jesus affirms the situation is dire from a sheer statistical point of view (Matt 7:13,14). Second non-negotiable:
2) salvation is available, only through Christ (John 3:36, Acts 4:12, John 14:6, Matt 21:31-33, John 5:24,25;1 Tim 2:5). This means if there is salvation, it comes by a gift of grace (Eph 2:8,9) not because we can work our way up to it or earn it by how good we are.
So by just taking these two non-negotiables, we avoid the situation where we start to ask, "but what about my good Buddhist aunt Emma?" or my "kindly old Methodist grandpa" or the "noble savage in Africa" etc - all attempts at heaven through moralism, while noble, are doomed to fail. The Bible says "God has bound ALL men over to disobedience that he might have mercy on them all" (Rom 11:32).
So if we can settle on that... then a BETTER question to ask, instead of appealing to the goodness of this or that non-Christian as a basis for salvation is this: can a person exhibit saving faith in Christ, and be saved by that grace without knowing about Christ or explicitly receiving him? It's a better question because it affirms the two non-negotiables above - all are lost in sin, and if people get saved, they get saved through Christ.
Less clear biblically, is who/how many/when people get saved THROUGH Christ without KNOWING ABOUT Christ. All Christians are agreed that this does happen. It is PRESUMED in the New Testament, that Old Testament saints are saved. Moses, Adam, Elijah, Abraham, these people are all presumed to be in heaven. How can they be saved if they never knew about Christ or expressed faith in him? Some say, well, as Jews, they implicitly hoped for Messiah, and they were covered under the temporary stewardship of the law and sacrifices which pointed ahead to Christ - true, but there are some non-Jews who had no law and no covenant sacrificial system who are also presumed to be saved: Noah, Job, Melchizidech.
What are the elements of saving faith? Humility (1 Pet 5:5b), contrition, repentance (Ps 51:17), acknowledgment of spiritual poverty (Matt 5:3), confession (Ps 32:5), trust in God's mercy (Ps 52:8). Can one have saving faith without the specific content of the special revelation in Christ and be saved on the basis of Christ's merits, while not knowing about them? I think we have to say it is certainly possible. Is this likely? There, I think we have say no. (Romans 10:14). This brings two more non-negotiables:
3) the evangelistic mission must be at the heart of every church. And
4) We are convinced that God's will is that ALL be saved (2 Peter 3:9).
So if there IS a way, we can rest assured, God will make a way! God is not baring the door. God WANTS salvation to come to as many as possible – and churches should reflect that heart!
When it comes to the first church and how this theology played out... you saw "good" God fearing people, who, because of their faith and hunger for righteousness, were filled. Cornelius (Acts 8) is one such man. God sees his faith and brings him the specific content of the Jesus message of grace which he eagerly receives and is saved. I know of many modern stories just like that, where those from non-Christian countries of the world seek God with all their heart and God finds a way to get the message of Christ to them.
So while responding well to the revelation one has may lead to MORE revelation, less certain is if the unreached can be saved without ever hearing the Message fully. Maybe not. Our agnosticism about the destiny of those people should keep us humble - we can't judge their souls, nor do we have all knowledge (1 Cor 13:12) - but this we know!: That when a human bows the knee of their heart to Jesus, they receive new life. So while we suspend judgment on how our fair God (“will not the judge of all the earth do right?” - Gen 18:25) will process the unreached, Christians know what our own predicament was before Christ... we were lost. Are the others so different? So we are motivated to get the Word out.
One more thing must be said: if it is God's earnest desire that every person be saved, we can be sure that geography is no obstacle. This is where we have to eschew the idea that Christianity is white, or western or European. It is not. Never was. For 3 hundred years it's best thinkers were African! The Coptic church is the oldest church that survives still in Egypt, North Africa and the Middle East. There is evidence that the gospel may even have stretched as far as China in the 7th century, to India in the 1st!
And besides that, God is not bound by religious upbringing like we think he is. Saving faith is influenced by, but not the same thing as your upbringing. Paul even said to pagans living outside of the Jewish stream of revelation, Acts 17:26-27 "From one man he created all the nations throughout the whole earth. He decided beforehand which should rise and fall, and he determined their boundaries. "His purpose in all of this was that the nations should seek after God and perhaps feel their way toward him and find him — though he is not far from any one of us."
This means being born a Muslim or Buddhist in a non-Christian country is not an "accident". It's by God’s design - the purpose? SO THAT MEN WOULD SEEK AFTER GOD and find him! Geography is no "curse" in this process. It may be MORE likely a person finds Christ in India than in Indiana! We all know people whose involvement with a "Christian" upbringing was no help to them finding relationship with Christ. But for the truly penitent, spiritually bankrupt, pure in heart - they shall see God, Jesus said, and evidently Paul thought their geography was no insurmountable obstacle.