Non-metal pet access door flaps; non-metal pet doors; assemblies comprised of a non-metal pet door and a non-metal pet access door flap; non-metal pet doors, non-metal pet access door flaps, and assemblies comprised of a non-metal pet door and a non-metal pet access door flap, all for mounting in doors, screen doors, sliding doors, insect screen doors, security screen doors, windows, window screens and sliding windows