That's your experience as a mechanic handling damaged spinners, or the cracks that result to cowlings, or prop flanges, or your experience as a guy that's pushed on the propeller?

I fly lean of peak; I do it all the time, when appropriate (it isn't always). I also judiciously use the propeller, when appropriate.

I've seen cowlings damaged, spinners damaged (and that have failed), and propellers damaged from pushing and pulling on the propeller, and I know two individuals who suffered head injuries when struck by a prop after moving it.

I've seen a lot of people push on the spinner, on the assumption that rather than apply asymmetric forces on the propeller by pushing on one blade, pressure on the spinner is along the thrust line of the engine. The spinner is decorative in many cases, in many others it's important for engine cooling and part of the design for the pressure cowl. Regardless, it's easy to get out of balance, to damage a backing plate, or to misalign the spinner or deform it by pushing, and it's a way to start cracks, too. I've seen each.

When I install a spinner, I use a torque screwdriver and take pains to ensure it's aligned, and check it in operation; imbalance or misalignment can cause failure, which can lead to propeller and aircraft damage. Pushing on it can be part of that.

I don't know any propeller manufacturers that recommend pushing or pulling the aircraft by the propeller, and I'm not aware of any engine manufacturers that make that recommendation, either. I'm aware of a number of warnings and cautions by different manufacturers against moving the aircraft using the propeller.

In small aircraft that are easily maneuvered, it may or may not present a hazard to the prop, crankshaft, prop flange, seals, and bearings, but then again, it may. It's always a good idea to avoid handling the propeller any more than necessary, regardless of the mag status. One needn't be afraid of the prop, but it should be respected.

I've seen more than a few people grab the prop tips to push or pull; definitely a bad idea.

Some have said that one can't apply as much force to a propeller by pushing or pulling as is applied in operation, but that's not an accurate statement. The force applied to a propeller when static is not at all the same as applied to the prop during operation. When pushing or pulling on a static prop, a direct moment is placed on the blade and shank on a specific direction, with no centripetal force acting on the blade. The actions on the propeller, shank, hub, and seals are quite different when the propeller is "pulling" outward as the prop spins. The rigidity of the propeller and the stress it experiences are quite different in operation, than when static. Is it going to break off in your hand? No, but that's irrelevant.

The strength and characteristics of a propeller in a static state are different than when it is in motion, and the lack of centripetal force on each blade when the push/pull is applied by hand does not mirror the force acting on the blade when the prop arc is developing thrust in operation. It's best not to compare or confuse the two.