Whether people believing in a hypothesis is evidence for the hypothesis depends on the hypothesis. If the hypothesis does not contain a claim that there is some mechanism by which people would come to believe in the hypothesis, then it is not evidence. For instance, if people believe in a tea kettle orbiting the sun, their belief is not evidence for it being true, because there is no mechanism by which a tea kettle orbiting the sun might cause people to believe that there is a tea kettle orbiting the sun.

Bad example. In fact, the example you give is sufficient to require that your contention be modified (or rejected as is).

While it is not the case that there is a tea kettle orbiting the sun (except on earth) there is a mechanism by which people can assign various degrees of probability to that hypothesis, including probabilities high enough to constitute 'belief'. This is the case even if the existence of such a kettle is assumed to have not caused the kettle belief. Instead, if observations about how physics works and our apparent place within it were such that kettles are highly likely to exist orbiting suns like ours then I would believe that there is a kettle orbiting the sun.

It so happens that it is crazy to believe in space kettles that we haven't seen. This isn't because we haven't seen them---we wouldn't expect to see them either way. This is because they (probably) don't exist (based on all our observations of physics). If our experiments suggested a different (perhaps less reducible) physics then it would be correct to believe in space kettles despite there being no way for the space kettle to have caused the belief.

P(religion is true | overwhelming professing of belief) > P(religion is true | absence of overwhelming professing of belief).

In other words, I think my two formulations are isomorphic. If we define evidence such that absence of evidence is evidence of absence, then one implication is that it is possible for some evidence to exist in favor of false propositions.