"It does not matter how just, kind, and generous they have been with their fellow humans during their lifetime: if they do not accept the gospel of Jesus, they are condemned. No just God would ever judge a man by his beliefs rather than his actions."
It is difficult, if not impossible, to provide a satisfying answer to this challenge. After all, even for believers, the doctrine of hell is difficult, and goes against our own inclinations - to forgive ourselves, to lessen our own culpability, to judge ourselves as "basically good." It's only by resort to Scripture, and a bit of philosophy, that we affirm that a just God must have a place of punishment if there is to be such a thing as free will.
A "just" God does justice, which means to punish or reward appropriately. In the Western tradition, we punish people for the actions they commit, but the extent of punishment is dependent also on the person's mental state, and a person's mental state is reflective of his or her beliefs. Premeditated murder is worse than manslaughter, and is punished more severely, and a hate crime is a sentencing enhancement that adds more punishment to the underlying crime. In both examples, a person's beliefs are at play: the premeditated murderer has reflected on his choices and wants the victim dead; a hate crime reflects a belief that the rights of a member of the protected group are especially unworthy of respect. So, considering a person's beliefs may well be relevant, especially if those beliefs have motivated the criminal behavior.
But the challenger's mistake is even more fundamental. He is wrong to assert that people are condemned for not accepting the gospel. Christians believe that people are condemned for their sinful behavior - the "wages of sin is death" - not for what they fail to do. The quoted challenge is like saying that the sick man died of "not going to the doctor." No, the person died of a specific condition - perhaps cancer or a heart attack - which a doctor might have been able to cure. So too with eternal punishment. No one is condemned for refusing to believe in Jesus. While Jesus can - and does - provide salvation for those who seek it, there is nothing unjust about not providing salvation to those who refuse to seek it. After all, we don't normally feel obliged to help someone who has not asked for, and does not want, our assistance. So too the Creator has the right to withhold a gift - i.e. eternity spent in His presence - from those who would trample on the gift, and on the gift-giver.
The quoted assertion also demonstrates an unspoken belief that we can impress God with our "kind" or "generous" behavior. This fails to grasp what God is - a perfect being. We cannot impress Him. What we do right we should do. We don't drag people into court and reward them for not committing crimes. This is expected of them. They can't commit a murder and then claim that punishment is unfair, because they had been kind and generous in the past. When a person gets his mind around the idea of what perfection entails, trying to impress a perfect Creator with our "basic goodness" no longer seems like such a good option.
So, in the end, we find ourselves in a predicament. We use our free will to rebel against our Creator, but we want Him to accept this rebellion, and us, with "no questions asked." When God judges us, He finds us wanting in both our actions and our beliefs. But in His goodness, He also provides a solution to our problem, a bridge that gaps the divide that exists between us and Him. There is nothing unfair in any of this.
After all, entry onto that bridge is free, and available to everyone. But we must first want to cross over.