For clarification, in baseball I believe it is generally considered permissible to support a team from the same league in the post-season (this is especially true of National League fans, who are morally obligated to oppose any AL team in the World Series on the assumption that this team will very often be the Yankees), but only if the team is not a division rival.  The more bitter of a division rival the team is, the less acceptable supporting their post-season play will be.  Supporting your team’s historic, bitter division rival is obviously entirely unacceptable.  Doing so as part of political pandering should normally result in deportation, but standards are slipping.

P.S.  There is one gray zone, which may permit supporting the team that defeated your team in the latest round of the playoffs on the grounds that you may find some consolation in having lost to the overall champion, but this is generally viewed as a weak excuse.  This does not usually conflict with the no-support-for-division-rival rule, since it is relatively rare, even with wild cards, for division rivals to meet in the playoffs.  If there is a direct conflict, as there was in the Yankees-Red Sox matchup a few years ago, the division rival rule obviously takes precedence.

P.P.S.  There is also a general New York exception for all non-New York fans, which means that in the event that either New York club reaches the World Series or (horror of horrors) there is a subway series, it is not only permitted, but positively encouraged, for them to support the non-New York team or simply pretend that the entire thing is a bad dream.