Censorship is not limited to the destruction and prohibition of things you don't like, although that is the sense that it is most often used in these days. In the past censorship also referred to disapproval, that is, simply saying that you don't like something. The implication is that this will make the person who did it to be less likely to do it again. The more people who let you know (directly or indirectly) that they are against whatever you are doing, the more likely you are to stop. Gossip would be one of the most fun and effective examples of this type of censorship.
This kind of censorship is probably necessary to make it possible for humans to live together, and is therefore most likely a good thing.
The question is how much and how formalized good old fashioned censorship should be. Does peer pressure really need to be replaced with a dress code? Is an organized protest the same as a letter to your congressman? Is it okay to yell out epithet in the street, or should you limit yourself to dirty looks?
When arguing about censorship people often accuse someone of censorship in this older sense, and then attack as if it were the same as the newfangled 'modern censorship'. Needless to say, this is a fallacy.