popular opinion as evidence

[Coffee Jesus]

Which is exactly why "common sense" is fraught with error. Without independently testing or verifying these claims, all sorts of "common knowledge" can be accepted without actually being true, and it's important to evaluate claims used to support other claims.

But we cannot always evaluate their reasoning for ourselves. In such cases, we will have to consider the probability that they had good reason to believe it.

I could accept that there are some default counterarguments to ad populum appeals that must be overturned before the appeal is valid. For example, bad logic could be a default coutnerargument. Whatever the claim is, the ad populum appeal is not valid until they show that bad logic probably wouldn't account for all of the observed popularity. But even then, we could throw on other counterarguments, like hallucinations, liars, etc. Anybody who wants to make a valid ad populum appeal will likely have an arduous task ahead of them.

And yes, the fact that there are god concepts in existence DOES make it more likely that there are gods than the probability would have been if humanity had no god concepts.

Yes, but that sort of reasoning is useless unless we have established the expectation for the false condition. After all, if we had reason to expect that many people would believe in gods even if there were no gods (null hypothesis), but then nobody at all believed in gods, that would be inconsistent with the null hypothesis.