the ability to protest carries with it the right of ones message to be heard. you shouldn't be able to just de facto shut down protests by coming up with "can't disturb ________ " rules. what, we can protest but only 20 miles from our target in a sound proof cube? i mean we can still assemble and we're still protesting. clearly that would be seen as an affront to ones right to assemble and protest.
the question of course being how far that's allowed to go in either direction.