this is a fascinating coincidence as I was discussing Matt 25:34-40 with my conservative/neo-Calvinist friend the other night. I took a position much like Ernest's, that the text can be read to mean 'salvation outside the Church'. he took the position that salvation is only received sola gratia and sola fide, that good works earned you nothing, and in fact that good works inspired by an ethic other than faith in Christ is actually a sin against God.
his counterpoint to the Ernest-argument is to emphasize that Christ is addressing those who already believe in him, and that his words do not apply to those who do not accept Him as their Savior.
The problem with both of these arguments is this text does not explicitly address the consequences of having belief versus not having belief. Even though the sheep and goats happen to be believers in the parable, some of them, for all we know, may have not been believers by faith. Some of them could have been skeptics all their lives. Some of them could have come to believe by actually
being shown the way at some point in their existence. We, as the readers, do not know. I tend to avoid seeking answers to questions by interpreting parables that may or may not address them, and I don't think Matthew 25:31-46 teaches us anything other than that we should do good works.
The only part of the New Testament that even hints at the question of non-believers' fate is when Jesus appears to Thomas. Though Thomas' appearance is brief, people (especially atheists/agnostics) can probably relate to him better than any other character in the New Testament simply because they don't want to believe anything that cannot be proven by scientific observation. Thomas didn't come to Christ through faith, he came to believe only after Jesus showed him tangible evidence of his divine nature and resurrection - the nail marks in his hands. When Thomas doubted, Jesus didn't condemn or reject him like how so many Christians treat skeptics today.