We've seen a lot of people hopping ship between leagues over the last two elections. While it's totally fine to be politically sketchy as all hell, it is pretty blatent in a lot of cases.
I'd suggest that if you try to join a league while having held membership in another one before, the Official request a hefty, though not crazy, bribe to overlook your past affiliations.
It fits the themes and ideas of the setting, makes sense for them to do, and allows for people to switch around Leagues still without making it something to just do on a whim.