Well, speaking from the perspective of both an activist and a political staffer, protesting in and of itself is not rude, I don't think, but there are ways to do it politely and ways to do it rudely.
where I work, there is an area outside where many protests take place, it's well trafficked and the background is symbolic for the news cameras. That's fine, but it's also an area that is a major walkway for staff members trying to get from one place to another in the course of their daily duties.
When protesters block the way of staffers who just want to get their lunch, that's rude. Particularly when you have no way of knowing if that staffer happens to agree with you or not.
I was once marching in a protest that was a counter to another, larger protest on the same day. I am proud to say that our designated area was picked up when we adjourned. Our leadership was determined to leave a good impression, and that included not littering. I can't say the same for the other group. Additionally, as I was marching, ignoring the participants in the other protest (our opponents) as was, I felt, proper, one of them got in my face and spit on me. I don't care what your views are, or how much you despise mine, there is never a good reason to spit on me. Particularly when I didn't even acknowledge you were there, much less provoke you.
Obviously there's other examples that could be used, but really, it just comes down to the golden rule, which all etiquette does, in a sense.