Sadly, the insults of those we do not respect often matter, because of what they imply about that person's future conduct, and because of their effects on third parties.

So for example if a bully starts insulting you, this may matter, both because this might indicate he is about to attack you, and because it may cause other people to turn against you. To give a non-cyber-bullying example, the insults of Idi Amin against Indians residing in Uganda surely mattered to them, even though they did not respect him.

This seems inapt as a generalization about human psychology.

In one psychology experiment which a professor of mine told me about, test subjects were made to play a virtual game of catch with two other players, where every player was represented to each other player only as a nondescript computer avatar, the only input any player could give was which of the other two players to toss the "ball" to, and nobody had any identifying information about anyone else involved. Unbeknownst to the test subjects, the other two players were confederates of the experimenter, and their role was to gradually start excluding the test subject, eventually starting to toss the ball almost exclusively to each other, and almost never to the test subject.

Most test subjects found this highly emotionally taxing, to the point that such experiments will no longer be approved by the Institutional Review Board.

In addition to offering a hint of just how much ethical testing standards can hamstring psych research, it also suggests that our instinctive reactions to ostracization do not really demand identifying information on the perpetrators in order to come into play.