This completely depends on where you're from and where you live. If you live halfway across the country and you've adopted 1 or 2 teams from a specific city, then no its not weird to root for another city's teams in some other sport. Maybe I'll give you a pass if you lived in Boston until you went to college or something and never really liked basketball or Football. Then it's probably semi-normal to stick with most Boston teams but root for the team from wherever you end up in that other sport.
But yea its batshit crazy if you're from Boston and grew up in Boston and spent any part of your adult life in Boston to cheer for the Red Sox, Celtics, Bruins and Cowboys or something.