For my experience, pulling on any propeller blade tip is an absolute no no. I cannot see any good reason to not grasp the blade as close the hub as is possible. When I pull on a prop, my hand will be touching the spinner.
Now, if you have a variable pitch propeller, more caution is warranted - but, there are few variable pitch propeller equipped aircraft which are still light enough that moving them solely by hand on the propeller works well. Yeah, Cardinals, Arrows and a few others are on the size line, but you get the point... Find a tow bar!
I was treated to a tour of the MT propeller factory last week - I was extremely impressed with the quality and care of manufacture. They are good, well designed, tough propellers, but I really cannot see myself pulling on one of their blades. Not because I'm concerned I would damage it, but more 'cause it's kind of like pulling on a piece of art!
I'll pull on a solid metal prop, on a very light aircraft. Any vintage wooden propeller aircraft I have flown has other better places to pull, and any variable pitch usually has a towbar, or other suitable means of moving it as intended.
I have zero concern that when moving a light aircraft with ONE HAND on the INNER part of the blade of a SOLID propeller, I will harm the engine. Imagine the gyroscopic forces put into the crankshaft by the inertial of the heavy propeller during hard maneuvering. You could never equal those with one hand on the inner blade.
Helicopter rotors? Very little comparison there. True, we do not handle helicopters by their blades. But their blades are much more delicate than any propeller, and employ tip weights to benefit from centrifugal forces. Propellers don't really work that way.
If you ever get the chance to ride as a passenger in a Dash 8, sit in the plane of the prop, and watch the blades flex forward as the pilot puts up the power, they move a surprising amount forward!