Bare Ground Wires
Basically the metal cases on *everything* electrical should be grounded, so no problem with a bare ground wire touching any metal case/box. Also it is less expensive to manufacture the wire.
Now if a bare ground wire were to contact a "hot" conductor, then this would trip the breaker*. Or if a "hot" wire were to contact a bare ground wire, then this would trip the breaker.
The best part of all this is if a hot wire (say in an appliance like a range) were to touch the metal case of the appliance, then this would trip the breaker. This is a neat feature about grounding. It will either trip the breaker or at least keep the "short" at "ground potential" so people are protected from being electrocuted.
As to wiring outlets, I like to connect/bend the ground wires so they will go to the back of the box when installing the outlet. Keep them away from the front sides of the box.
As for insulated green ground wires, you will see this on appliances with stranded wire cords where everything can be moved, dropped, twisted, etc. In this case you wouldn't want a ground wire to go flying around inside the appliance and possibly contacting a hot connection.
*Assuming everything is wired to modern code.