DJI FlySafe will let you fly in places that require FAA authorization. You need to check the FAA UAS facility map and if necessary get authorization from LAANC before flying. DJI FlySafe is a different set of restrictions that don't correlate to FAA airspace restrictions.

Just because a drone doesn't need to be registered does not mean it's not required to follow FAA regulations. All drones regardless of size need to follow FAA regulations when flying outside.