The twist in a prop blade is to keep the AOA of the blade something sensible along the length, rather than manage lift distribution per-se. The tips are travelling 'round' a *lot* faster than the roots, whereas both are travelling 'forward' at the same speed. Consequently the tips 'see' the airflow coming from a rather different direction.
As for pushing, I don't believe it. Think for a second what forces go through a prop when you're manouvering with a lot of power on. The only scenario I can see is that the composite/wooden props on some of the microlight/LSA types could be susceptible to (trailing edge) damage perhaps, just through rough handling? Spinners certainly fragile, but in most cases I'd be more worried about people pushing on inappropriate airframe parts than the prop.