> If the actions and beliefs of a group are fundamentally morally repugnant to me, I think that it is reasonable to not expect me to be able to find "something positive" in it.

I'm not sure you appreciate how symmetrical this statement is. You are on Team A, saying it about Team B, but nothing in the statement actually depends on that permutation of teams -- it could be equally compellingly said by a Team B member about Team A.