Do Real Madrid soccer fans also root for the Real Madrid basketball team by default?
lol, they definitely do in Madrid (lived there a couple of years).
if you said sthg like, i am Real in bball but ,ehm, barcelona in soccer, ppl would just die laughing.
same story with all franchises that have both bball and soccer clubs (common in greece, spain and some other european countries, but not the case in northern europe, france and italy): for example panathinaikos, cska, maccabi etc
only exception is international fans of madrid- say a russian who supports real in soccer is obviously under no obligation whatsoever to do the same in bball.
Incidentally, from what I read here, city affiliation is stronger in the states than in europe (esp. in bball). I suppose the reason is there are only three-four good teams in every country in Europe, so the choices are more limited (and the distances shorter anyway).