I would like to point out a few things here. First of all, considering the very title of this thread, it seems that this question is primarily concerned with addressing Christian thoughts about this topic. And as a Christian, I can only offer the perspective I have on the subject.
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Here's a new outjet for the thread: What about people who've never been introduced to Christianity (half of the world, for example)? How are they judged in the afterlife?
In other words, can people who have never heard about Jesus reject or accept him? That I cannot answer. But I will say this: it certainly stands as a challenge to us Christians to get busy with the work of making disciples of the nations. At the same time, though, it also stands as an indictment against those who oppose the spread of that word. The issue for me is this: people who do not know God are alienated from him already. The only solution for this alienated condition is reconciliation. Asking how they are judged does not really help in understanding this.
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And what about the people who aren't sane enough to accept God?
Again, I cannot answer for them. I assume you mean primarily people who do not have the mental capacity to understand even the basic message of God's love for them in Christ. I work in a dementia ward, and many of the people there are barely able to articulate a coherent sentence, so I can certainly understand the concern. I have two answers: 1. Jesus does commend "the faith of a child." That is, faith should perhaps be better understood as trust, rather than theological aptitude. 2. We can always rely on the power of the Word to accomplish what God intended, even if we are unable to see the result. I have a third, which I am not sure all Christians can fully understand, and that is Sacramental Grace. God did promise to work through the Sacraments (particularly Baptism), and I do not believe that it is entirely dependent upon a person's understanding of what they are receiving.
You are right, though. There is no proof that God even exists. But just as with anything else in life, you will never be given a 100% absolute answer beforehand. It is a risk. But isn't that true with just about everything else in life? You ask a girl or a guy out, knowing full well there's always the chance they'll say no. You get in your car and drive, knowing full well there is at least a slim chance you might be in an accident. You buy an article of clothing, not sure whether it will fit you right after you wash it. You decide on a career, not knowing whether you'll be good at it until you are at least moderately trained for it. I could go on, but you get the idea. No, God doesn't prove his existence beyond doubt, but it is interesting that we don't place that kind of demand on anything else we encounter in life.
madefromthebeststuf, you might be right about it being up to chance. But not entirely. There are plenty of people in this world who have become Christians, even though their families weren't. There are also plenty of unbelievers in this world whose families were Christian.
In previous posts, I have pointed out that I am not sure that discussing who deserves what is very helpful at all. All I know is that, whether deserved or not, people are in a certain condition that leads one way or another. Those who are going to heaven most certainly do not deserve it, as most of them would say if you were able to ask them.
But I do have a thought about that: are you willing to try it? If there is a God, then he must care about anyone who in their hearts wanted to know him, even if they did not fully understand him. As I stated above, it's not a matter of knowing your theology perfectly, but of trusting in him who calls you. If you truly wish to find God, simply begin by admitting, "God, I don't know you, but I'd like to." I cannot say for certain (after all, I cannot foresee what resistences there might be later), but God might just show you the way to find him, if you are willing to follow where he leads.
In agnosticism, I see a kind of humility that is somewhat commendable. It is simply the realization that we do not have all the answers. But there is this danger: it also does not lead anywhere. Leaving an offer on the table indefinitely doesn't accomplish any more than outright rejecting it. I am convinced that true humility is the realization that we are helpless before God, and that we simply do not deserve the gift he has to offer us. The race of humanity is already alienated and estranged from God. God has already done all that can be expected of him to reconcile that broken relationship. I do not think we can or should demand more.