Is there a single word which denotes immunity from scrutiny or criticism? It would be something with mostly negative connotations, implying some dogmatic or intolerantly axiomatic context which excuses a certain idea or idea bearer from being scrutinized.
Perhaps the word you're looking for is sacred cow:
one that is often unreasonably immune from criticism or opposition
Google's definition also explains that this term originated from "the Hindus' respect for the cow as a sacred animal". Hence, anything or anyone which is a sacred cow is seemingly immune to criticism.