The theory described is a theory of incredible snobbery! First of all, the person described thinks that there is a “‘ proper’ enjoyment of art” (and, presumably, an improper one as well). He thinks that “untrained” people viewing art enjoy only “a baser pleasure,” and calls other people “museum ‘tourists.’” In the first blank, “hoi-polloi” matches the idea of common people, the masses. A “cabal” is a secret political faction, so is unrelated to this sentence. “Literati” are well-educated people who are interested in literature; this is nearly opposite the meaning required in blank (i). The second blank is a description of the “sensibilities” of “the museum ‘tourist,’” and “parochial” matches the idea of ordinary, low-class, unsophisticated. “Incendiary” can literally mean designed to cause fires, or can figuratively mean exciting or provocative. Neither works here. “Dulcet” means sweet and soothing, and typically refers to sound, not to a noun like “sensibilities.” Finally, “the art theorists and art historians” are thought to have “a facile,” or overly simple, view. The theorist seems to think that only “pure aesthetics” (principles of beauty) should matter; the theorists and historians he disdains are those who like “cultural referents or narratives”— that is, recognizable themes or figures, or stories. Both “an urbane” (suave or sophisticated) and “a painstaking” (meticulous or thorough) are positive, disagreeing with this person’s attitude toward “art theorists and art historians.”