It seems to me that people who do not identify as religious often see the comfort offered by religion as negative. Further, it seems that this comfort is regarded as constituting evidence against the authenticity of religious experience.
Am I mistaken?
I think that whether the comfort of religion is a good thing (to the extent that it's a thing at all - I think in many cases, it's not that religion itself is comforting, but more that it creates discomfort at the idea of leaving it) depends on whether it's true.
It's fine to be reassured by comforting knowledge, but if your comfort is based on something false or vacuous, then I think you're getting into "opiate of the masses" territory.
As for the question about evidence... I don't think it's really a matter of direct evidence that the belief is false; it's something else.
People do believe religious beliefs. Presumably, there's some reason for this. We can think of a list of all sorts of potential reasons for a belief including "they believe it because it's true."
Whatever our list of potential reasons, it's possible that we may eliminate all the others so that only "it's true" would be left so that even though it wasn't supported itself, it would still be the best tentative conclusion available.
However, if "they believe it because it's comforting" is still available, then there's no need to accept "they believe it because it's true" just because it's the only option available.