Were ancient people entirely uncritical of supernatural claims, or did they have ways of being skeptical or selective about such claims that are loosely comparable to how people in post-Scientific Revolution societies tend to be skeptical today?

I am asking this in a broad, comparative sense across pre-modern history, including ancient Near Eastern societies, classical Greece and Rome, and medieval Europe. I am not questioning whether supernatural beliefs were widespread, but how people related to them in everyday life. Specifically, I am interested in whether people tended to accept supernatural claims indiscriminately, or whether they exercised selectivity, doubt, or practical distance from such claims in ways that are loosely comparable, in an analogical sense, to attitudes that exist in modern societies.

In my experience at least, I think a lot of people think ancients were entirely superstitious, unthinking people when it comes to supernatural claims. I know that they did not have a scientific conception of the world the same way we do, but is there any evidence that subjectively they experienced the same sort of doubt we tend to have toward supernatural explanations of natural events, or mythical stories, etc?