Music Censorship will prevent other players' Rock Bands from entering your territory, making it helpful when one of your opponents is closing in on a Culture Victory. However, it will also impose an Amenities penalty on larger cities, stymieing their potential growth and productivity.
The initial reaction to every new cultural art form in each generation is for the previous generation to declare, with shock and horror, that a new art form is corrupting the public morals and leading directly down the steep and slippery slope to the end of all that is good. Because of this, the old generation declares, the new art form must be banned for the public good. If there are any universal human experiences beyond death, taxes, and war, then intergenerational fights over culture are a strong contender. Rock music in particular seems to have come in for its fair share of criticism during its explosive growth during the Twentieth Century. The tension between fun- and music-loving young people and their censorious elders has become something of a trope in the west, and any attempts to ban music generally seem doomed to failure, or perversely encourage interest in the forbidden fruit. Whether laws specifically banning the sale of music by western musicians inside the Communist bloc of nations, or conservative western elements banning (even oblique) references to canoodling, these measures are generally regarded as quixotic failures by The Man.