The story
From moon + bat. Originally the name of the XP-67 experimental aircraft, developed by McDonnell Aircraft in 1941. Used in the 1940s by the science-fiction writer Robert Heinlein, then used in the term “barking moonbat” coined in 1999 by Perry de Havilland of “The Libertarian Samizdata”, a right-libertarian weblog. This originally referred to both left-wing and right-wing crazy people. Sometimes wrongly claimed to be a corruption of Monbiot (from George Monbiot, British environmentalist and Guardian columnist).
Etymology from Wiktionary, CC BY-SA 4.0.