Rather than left or right, it's a conservative's thing: left conservatives censor on ideological grounds, such as "racism", "sexism" or the catch-all "promotes discrimination", while right conservatives censor on moral grounds, such as "promotes sex", "promotes violence", and the catch-all "corrupts our youths". They'll both censor anything made by a recognized member of the opposite sector, though, regardless of actual content. Similarly, it's opposed by liberals on both sides of the spectrum, such as anarcho-colectivists on the left and anarcho-capitalists on the right, both of which see state censorship as a much bigger sin than anything you may possibly write or record.
Of course, they seldom admit as such when confronted with it; often they'll claim is for protecting impressionable people ("they're taking advantage of people!"), consumer's rights or even freedom itself ("people should be free to go to a bookstore without seeing $X!"), but test them on the alleged "value" of a few sampled works and authors and the old party lines should soon become apparent.