Your question doesn't have a clear yes or no answer. In general you want to tape anything that can be damaged by your polishing. Plastic trim gets stained, so that is an obvious yes. As for raised, painted body trim, if you are doing aggressive polishing it is probably a good idea as it is easy to damage it without realizing until it's too late. A lighter polish has lower risk, but the risk is still there, depending on technique. The painted plastic, like the door pillars is the same scenario. It is often very soft paint so it should be protected from aggressive polishing, but light polishing should be okay.
Remember, a roll of tape is usually A LOT cheaper than a repair. When it doubt, play it safe.