Communism was a political and economic ideal and philosophy that was embraced by several Earth nations in the 20th and 21st centuries. The pillar of the Communist philosophy was equality and pre-planned economy. Nations that embraced it included the Soviet Union and China. Slang terms for a person who followed this ideal, better known as a communist, included "pinko", "red", and "commie." It was the clash between communism and capitalism that drove the Earth Cold War.
In an alternate timeline, Lenin was assassinated by an unknown assailant in 1916, and no one managed to take his place. As a result, Russia never turned to communism. (ENT: "Storm Front, Part II")
In 1953, Douglas Pabst insinuated that Herbert Rossoff was a proponent of communism. (DS9: "Far Beyond the Stars")
In the early 2020s, the Neo-Trotskyists came to power in France, and by 2024 had failed to quell student protests, leading to the belief among higher-class Americans that "Europe [was] falling apart." (DS9: "Past Tense, Part I")
The Kohms of Omega IV were named from a corruption of the word communist, an example of Hodgkin's Law of Parallel Planetary Development at work. (TOS: "The Omega Glory")
In 2364, Q adopted the guise of a United States Marine Corps captain and cynically suggested that the USS Enterprise-D "go back to your world and put an end to the commies". (TNG: "Encounter at Farpoint")
In 2401, communist was listed as one of the results in Raffaela Musiker's search for the "red lady". (PIC: "The Next Generation")