My position is that no passenger should move another passenger's bag. You are responsible for enforcing neither the airline's policy nor rules of courtesy. It's perfectly fine to move something a few inches across the bin or turn around if it fits, but if you want to move something to another bin, call the FA to do it.

Remember that if the owner of the bag sees you handling it, and something later goes missing from the bag, you could very well be blamed for theft.