What you wrote is you want a GameObject to be both a Player and an Enemy. But an Enemy is already a Player. The MRO issue just states that if you had a field a in Player, asking for this field in a GameObject instance would be ambiguous: should it be the a from the first Player you inherit or the one from the Player you inherit through your Enemy inheritance?
But are you sure you don't want to use composition instead of inheritance, here?
class GameObject(object):
def __init__(self):
self.player = Player()
self.enemy = Enemy()
