Those beliefs don't propagate where they should, that's the issue, and universe doesn't care if you made an excuse to make it sound better. Those beliefs still have zero effect on inferences, and that's what matters. And when you get some of that weak "evidence" such as your Zeus example it doesn't go towards other hypotheses, but it goes towards Zeus, because the latter you have been prompted with.

Or when you process an anecdote, it would seem to me that with your qualitative Bayes you are going to tend to affect your belief about the conclusion too much and your belief about how the anecdote has been picked, too little (for contentious issues you expect anecdotes for both sides). Since you are doing everything qualitatively rather than quantitatively, that's an approximation, and approximation that breaks down for what is normally not called "evidence".

edit: I'd think, by the way, that a real deity and a made up deity would result in statistically different sets of myths, making a specific set of myths evidence either for or against a deity depending on the actual content of the myths. Just as a police report by the suspect where the suspect denies guilt can be either evidence against or for the guilt depending on what the suspect actually said and how it squares together with the other facts.

edit2: an analogy. Suppose you have a huge, enormous network of water pipes, or an electronic circuit. A lot of pipes, trillions. You want to find water flow in a specific point, or you want to find voltage at a spot. (Probability flows in an even more complicated manner than water in pipes or electricity through resistor networks, by the way, and numbers are larger than trillions). I am telling you that you aren't considering a lot of pipes, they have effective flow of zero where they should have non-zero. You're saying that no, you can have one thick pipe which is all the flows that you didn't even consider - a pipe that aren't really connected much to anything. As far as processing flows does, that does not even make any coherent sense.