That widespread beliefs can be wrong?

I take Galton as making the many-religions argument for atheism (often used against miracles): that the mutual inconsistency of religions tends to refute them all. ('If testimony is enough to establish the truth of miracles claimed by the Bible, why do you not admit the truth of Muslim, Hindu, or Buddhist miracles? And if you deny their truth, how can you accept the Christian miracles?' etc etc.) Note his description:

...It either compels us to admit that the prayers of Pagans, of Fetish worshippers and of Buddhists who turn praying wheels, are [all] recompensed in the same way as those of orthodox believers...

The supernatural justification of all these practices are different and mutually inconsistent, and if there is no divine mechanism behind prayer, then how can it accomplish things like improving the health of someone hundreds of miles away, much less anything like world peace? (The 'self-help' model of prayer predicts only extremely limited placebo effects.)