The taking-out of material that may offend others is called

It is censorship.  When a material or a program is deemed to offend a certain belief or group of people, media will pull it out of circulation since it does not want to offend anyone.  Some protests this because it is a blow to free speech.  However, if it cause a great deal of conflict, then it has to be removed or censored.

The taking-out of material which may be offensive to certain spheres of people would be called censorship. If you dislike something I write and you want it to be taken out (if I'm writing a book for example), you could censor me by throwing these things out of my book and you could argue that it had offended you and that you didn't want it to be in the book for that reason.