First of all, in the absence of any real evidence, conspiracy theories and religion can mostly be rejected simply on the basis of priors. However, as a general rule, many people believing something, especially if it's a vast majority, is decent evidence for a claim, and so the fact that many people believe something should cause you to update your subjective probability upward, to some extent.
The important point here is that the strength of that evidence has a very significant dependence on how people attained those beliefs. If you were to find that those beliefs were attained via some generally reliable method, e.g. scientific experimentation and dissemination via broad scientific consensus, this would cause you to further update your subjective probability upward, because it would be a strong sign that their beliefs correlate with reality.
On the other hand, if you were to find that their beliefs were obtained by, for example, using a ouija board, you would update your subjective probability back down because the evidential value of the other person's beliefs would fall to pretty much zero.
Basically, finding out the process by which people obtained their beliefs partly or wholly screens off the evidential weight of the fact that they have those beliefs.
If many people got the same belief from Ouija boards independently, I'd update my belief in Ouija boards.
Conversely, if millions of people believe the result of a single poorly designed study, that does not make their number very relevant.
I think what should undermine belief in religions or conspiracy theories is that these people all read the same books and watch the same YouTube videos.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
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