After spending years in sports marketing, and after kicking the question around with colleagues, we were relieved to conclude (unscientifically) that political ID was an almost undetectable and rarely reliable indicator of fan support. Interestingly, fans of teams may gravitate to a choice of media (CNN vs. Fox), but it may be a function as much of age or other factors than political lean. Other elements that may form a political identification -- geographic considerations, socioeconomics, race -- may influence ticket purchases, but fans just don't like their politics mixing with their fun time. A friend with the St. Louis Blues said they greatly regretted having hockey mom Sarah Palin drop the ceremonial first puck at a game in the fall of 2008. The backlash against the team, not from Democrats, but instead from fans who wanted a break from the political season, was intense - although the ProgressNow "player cards" handed out pre-game were priceless. Same response to the Scott Brown/Martha Coakley/Curt Schilling silliness earlier this year, and to some degree, John Elway's endorsement of John McCain.
Your own musings about the Duke/Butler contest likely confirm your gut suspicions about fans in general.... The good news, from my perspective, is that sports is still largely devoid of the political opinion that occasionally touches film and music stars. Human nature usually forces us to actually unite - on the side of the hometown team and/or the underdog!