This question makes me think that politeness is more an aspect of yourself than of the person you're interacting with. More "I am a polite person, in control of my behavior" than "this person is good and so deserves politeness."

My first impulse would be, yes, be polite at first, even while you are telling him or her that they should be thrown in jail. You can be polite even as you are strapping someone to an electric chair. Rudeness would be used only in reaction to their rude behavior, in a repeated-game-theory way.

But I'm not sure that 'politeness' and 'rudeness' is clearly defined. Some people might think 'because you raped that woman, I'm going to advocate that you be prosecuted' is rude; I don't. It would be rude if you added 'you bastard' to it, or gloated, etc. Understandable, but rude.