Personally, If I thought a friend was making a dink move I would tell them. Who better to let them know?
People are way to quick to make excuses for stealing. If there is a fixed rope that isn't causing problems by being in the way or been hanging there for ages and looking especially ugly or dangerous, leave it alone. If you must take it down, leave it coiled up hanging nearby or otherwise try to get it back to the owner unless it is clearly trash. The same goes for a neatly hidden stash. Sometimes it is just impossible to carry everything in and out every day.
That being said, I think it is obviously incumbent on everyone to keep their fixed gear to a minimum and their stash neat and well hidden. Heaps of tarps, rotting crashpads etc. is not OK. It shouldn't be wrecking other's nature experience. To get all uptight about an occasional fixed rope is just being anal though. If it was your own rope up would you be shuddering in disgust?
Hope you get the rope back, Al.