The evidence for science and against religious origin theories may be obvious to us now. But thinking historically, how is the current situation for laymen different between listening to scientists today vs. priests and scholars in the Dark Ages? In both cases, the uneducated layman sees that every learned person seems to agree on certain basic facts about the universe, and s/he has to choose to either believe that consensus or not. In the absence of an alternative explanation, how is the medieval peasant to know that thunderstorms are *not* the work of God/Satan, or that any number of "miracles" are not caused by what the learned fathers all agree is the cause? After all, it's the best explanation being offered for the phenomena observed. And without a dissenting voice, those scholarly explanations can seem awfully convincing, especially when they get into impressive theological or natural-philosophy jargon that you can only half understand. For many people, the experience today is the same, only with scientists replacing the priests, monks, etc.
Of course to those of us with at least some understanding of science, the difference is obvious; "science works", hypotheses are tested, etc. But to Joe Sixpack who never had an interest, all he has is the consensus of scholars to go by. But of course that consensus now conflicts with the consensus of his peers and the leader(s) of his religious community, so in that sense it's harder for him to believe in science now than it was for our hypothetical peasant to believe in religious explanations back in the day.