Credible/Honest Apologetics?

[Belacqua]

The only first principles an atheist has to accept, is that: the outside world exists, and other minds exist, and we are not a brain in a vat being fed false information. But again, I don't think this is a faith based position, since I have evidence.

As I understand it, many many people in history have reported religious experiences which, for them, constituted solid evidence that God exists. 

In other types of cases, such a large number of people reporting similar experiences would be considered good evidence. Atheists, however, reject the claims of all of these people. What principles do they use for this rejection?

I would say that they are interpreting the evidence in light of a theory. This is something like a scientific theory -- a structuring system through which claims are evaluated. The theory posits the principle that personal experiences do not count as good evidence if they are not backed up by different kinds of evidence -- the scientific kinds of evidence which scientists prefer. 

The principles provided by this theory, which posit certain facts about the world, provide the standards by which atheists reject the claims of millions of people, and settle on the belief that God remains unevidenced. Without these evaluative principles, used to reject people's claims, we would have to admit that the millions of people in history who have claimed personal experience of God do lend credibility to the belief in the existence of God.

So it's pretty clear that to be a thinking conscious atheist in today's world requires commitment to certain principles.