Rudeness...something to ALWAYS avoid?
I’m not sure anyone would be that concerned with being polite when the goal is to get someone to never interact with you again, at all. Perhaps you should be going for straight-forward instead. I heard this question recently from an acquaintance, and it did spark a bit of curiosity, since he provided no details as to the why for his feelings. I didn't know what to say at the time, but after a bit of thought, now I have a response:
There’s nothing rude about being dispassionately up-front with your request: “I’d prefer that we not talk to each other any more.” Then smile briefly and walk away.
The snag with making a request of this kind, however, is that it’s probably not going to be the end of the conversation. Most people would want to know why. Unless they already know why, based on your history with them. And only you know that.