Mike Fallopian (these names do not quit) is the president of the right-wing libertarian group the Peter Pinguid Society, which makes the John Birch Society look "left-leaning" (3.24).
Oedipa and Metzger meet him at The Scope, where he tells the story of the organization's founding father: a Confederate general who tried to open a second front in the American Civil War by attacking San Francisco, only to be scared off by some Russians and resign his post.
When Oedipa notices that the Society is using Yoyodyne's inter-office courier system to deliver their mail, Fallopian explains that they are opposed to government monopolies on mail. He says that he is writing a history of private mail in which he hopes to link the Civil War to the postal reform movement.
Oedipa goes back to Fallopian several times in the novel for advice. He is generally unhelpful (like basically everyone in this novel) but at least he doesn't feed her sense of conspiracy. The last time Oedipa sees Fallopian he suggests that perhaps the entire "Tristero Conspiracy" is just a hoax. Oedipa becomes angry, accuses him of hating her, and sarcastically suggests that he get in touch with Winthrop Tremaine, the nut at the government surplus store who sells Nazi uniforms. Fallopian tells her that they are already in touch.
As you probably gathered, Fallopian and his Peter Pinguid Society are a parody of the American right wing. The John Birch Society that Fallopian references was a radical conservative group in the 1950s (and still active today) that was super, super opposed to communism. The fictional Peter Pinguid Society takes it a step further: they are also opposed to industrial capitalism on the grounds that "it leads, inevitably, to Marxism" (3.28). Through the character of Fallopian, Pynchon uses his razor-sharp wit to lay waste to radical American politics.
Fallopian's name is a pun on the female tubes that lead from the ovaries to the uterus. It is also worth noting that the Latin word "fallor" means "to err." In this case, the pun contains a hint of meaning, since Fallopian has a very fertile (get it? eh? eh?) imagination that often leads him to make weird (and wrong) judgments and assumptions.