Presumably the conflict between an ostensibly scientific, materialist, atheistic reality of modernity and the non-empirical, spiritual, theistic reality of their faith. Though I think it's implicit in the criticism of religious believers that they resolve the dissonance by, e.g., rejecting scientific truths. And arguably the other side does the same, by rejecting the metaphysical; compare atheism to agnosticism, where the former rejects what the latter says it cannot logically do as core religious beliefs tend not to be falsifiable. Personally, I like F. Scott Fitzgerald's perspective--"the test of a first-rate intelligence is the ability to hold two opposed ideas in the mind at the same time, and still retain the ability to function." Dissonance is everywhere, including in the modern so-called evidence-based world, often inescapable, and perhaps even fundamental to the human experience.