Are you allowed to run bare copper ground conductor into a plastic gang box (20 amp bathroom circuit)?

Yes, but do not attach the conductors to the box. Connect the device grounds together, first, and then push them into the box first. Next do the Neutral conductors and finally the hot conductors.

Just to be clear, the bare ground must be part of a cable or conduit, not run alone.

Are you allowed to run bare copper ground conductor into a plastic gang box (20 amp bathroom circuit)?Why are you asking this? There has to be more to the story.

Can you give us some details about what it is you are trying to do?