'Immune from criticism' would mean no one can criticize you. 'Immune to criticism' would mean people can criticize you, but you can ignore it. The sentence is saying that although it isn't possible to avoid criticism, we can ignore it and not let it bother us. Hope that helps!

Yes, I feel Iggy has hit the nail on the head nicely. I will add an example. A powerful dictator would probably be immune from criticism. Anybody who tried might end up in jail. Therefore there would be no criticism. Someone particularly insensitive would be immune to criticism. All the insults and criticism in the world would be like water off a duck's back.