Conspiracy Nut

A “conspiracy theorist” has been derided as a “conspiracy nut” since at least 1971. The term “conspiracy nut” was popularized after the 1963 assassination of U.S. President John F. Kennedy and the 1968 assassination of Martin Luther King, Jr. “Conspiracy nut” was repopularized by the 1991 film JFK.
 
Similar terms include “conspiranoid” (since June 1992), “conspirazoid” (since May 1996) and “conspiratard” (since October 2004).
     
 
Urban Dictionary
Conspiracy Nut
n.
1) A person who believes the Rand Corporation, in conjunction with the saucer people, under the supervision of the reverse vampires, are forcing their parents to go to bed early, in a fiendish plot to eliminate the meal of dinner. Or, some variation on that theme involving but not limited to the following groups, people and events: Regular vampires, specifically gray or reptilian saucer people, the Antichrist, The Freemasons, The Bilderbergers, The Trilateral Commission, The New World Order, Skull and Bones, The Illuminati, The Kennedy (or any other) Assassination, The moon landing, The 9/11 Attacks, The Pearl Harbor Attack, Area 51, or fluoridation of drinking water.
2) Kathaksung
If you believe Trilateral Commission Satellites are beaming mind-control rays past your tinfoil hat, you’re a conspiracy nut.
by The Cabal Jun 21, 2007
       
Google Books
The Danziger transcript; a novel
By Carl Fick
New York, NY: Putnam
1971
Pg. 63:
You-re one of those conspiracy nuts, did you know that, Doc? Shadows behind shadows.
 
Google Books
December 1975, Texas Monthly, pg. 79, col. 1:
While recounting their troubles, the people of Southwest often resemble the conspiracy nuts who hang around so many newspaper offices, fitting every random occurrence into a seamless pattern of malign intent.
 
Google News Archive
9 September 1978, St. Petersburg (FL) Evening Independent, “In Pursuit of the Conspirators” by Ncoholas Von Hoffman, pg. 11A, col. 3:
Since the murder of the president, the term conspiracy nut has lost its original meaning of someone drawn to join conspiracies. Now it means someone who’s convinced there is one. 
(...)
Are conspiracy nuts nutty? Not really.