Must readers who detect things that cannot be not true give authors the benefit of the doubt by concluding that what seemed like non-fiction is actually fiction?
Concluding that it is fiction implies the author made the whole thing up. I don't see that as giving them the benefit of the doubt. I'd say, supposing that the author made a mistake, or simplified, or extrapolated, or whatever, would be more charitable; that the author's intent is still honest and the rest of what they wrote may still be valid and useful.
For example, there are wildlife documentaries about lions hunting, that actually cut together scenes from several different hunts to make a coherent narrative, without informing the audience they have done so. The result isn't literally true, but still shows the lions' general behaviour in a truthful and useful way. All journalist includes distortion, because of editing; not everything can be included. You have to decide whether you trust the journalist.
Where does religious or spiritual writing fit into this consideration?
Hard to say without an example. If I catch them out in a minor detail, then it's the same as above. If it's a major detail that they know is impossible but are claiming is a miracle or some such, then, in my view, extraordinary claims require extraordinary evidence. I am not much inclined to cut such authors much slack. I am pretty much starting from the position that they are, at best, misinterpreting whatever they saw anyway.