It is easy to prevent tree damage and Leave No Trace when camping. A simple item like a bandana or sock can make a big difference. There are also "tree hugger" straps made from nylon webbing that can more evenly distribute weight when using a hammock and prevent tree damage. Also for recreational tree climbing, friction savers or cambium savers are helpful in protecting fragile tree bark from damage.
Just FYI the knot used above is the tautline hitch and will hold tight under pressure.... thus helping to keep the tree safe from impact.