The mystery move – examples please

I am looking for examples of how people attempt to protect their belief system – immunize it against rational criticism – by appealing to mystery.

Religious examples are good (do provide them), but I also want non-religious examples, e.g. people dealing with apparent scientific refutations of the claims of crystal healers, etc. by suggesting that science is limited in its scope and we must acknowledge “there are more things in heaven and Earth than are dreamt of in your philosophy, Horatio”, etc.

If the examples can be accessed on the internet, that helps. It’s for forthcoming book. I imagine there are skeptical websites that have many examples but I am struggling a bit to find them…