I think it depends on the situation and which fantasy team is currently the most important to succeed in my opinion. If for example, the Dodgers played the Giants and I had Tim Lincecum on one of my rosters. Somehow a Lincecum win and a few K's would be the difference maker in one of my H2H leagues. I look at it as somewhat of a win-win situation in that I'd be fine with either outcome (a Dodger win or a Lincecum win). The best-case scenario is Lincecum gives me a quality start and there's a win involved for either side (again, a Dodger win or a Lincecum win). Now actually cheering explicitly for the Giants because Lincecum did well is a no-no.
Now, I still consider myself very much an avid Dodger fan but the difference is I don't quite live and die by the results like the same way I would as a Lakers, Manchester United, or FC Barcelona fan. For that reason, I don't play fantasy basketball because cheering for anyone except the Lakers isn't quite right. I do play fantasy soccer (the Premiership and La Liga), but those fantasy teams are a very, very distant second to United and Barca as to what's more important. When it comes to fantasy baseball, I do side with my fantasy baseball teams more simply because fantasy baseball is the most fun to play and win. Plus, the Dodgers can't amount to anything anyway; they've mucked up many a good thing since 1988, why expect any different.