What follows are some facts…and a lot of speculation! To be honest, this is mostly headacanon, and totally open to debate! I love discussing this stuff. Hang on, this is gonna be long (no pun intended).
The Long clan, to which Wufei Chang belongs, found it’s home on colony L5 A0206. On Earth, they were probably a powerful entity before they went into space. They were forced into exile by whoever was in charge (I’m guessing the government of China in the series).
But how powerful were they? Well, we don’t know, but judging by the times I’m assuming it was a combination of political influences, monetary/corporate influences, and perhaps a growing influence over the masses, which probs contributed to the established government of the area disliking them, especially if they were rivals. They couldn’t have been powerful enough for a government take-over, not yet, since the establishment seemed to have no real opposition in exiling the clan. Perhaps they were a fledgling movement that was gaining power, but were stamped out too soon.