Should vents protruding through the roof be protected from weather?
Vent pipes no, the pipes are supposed to the set so any rain that enters, drains down the same as any water that enters the pipe from the sinks, tubs, toilets etc.

Intake pipes are only to take in air, not water and if there is a low spot in the pipe, water may eventually block the pipe like a water trap, so they need to be protected from the weather.