Dris was my first character, and as such I had no idea what I was getting into with regards to the matari tribal thing. So I made her grow up in a remote colony where there WASN'T a tribe that she could call her own. Her parents had their own customs, of course, but then again so did every family in the colony, and they were ALL different, so there was no cohesive unit to look to for answers.
Where this would come into play now is that she's adopted Syn's tribe as her own, and if that were to fall apart Dris wouldn't necessarily be affected, but Syn WOULD, and THAT would cause some definite issues. However standing on her own, and not regarding the issues with her mate, the change in faction wouldn't cause her any undue stress. Mourn the loss of her races' culture, yes. But her day-to-day activities wouldn't change (the ore must flow).
As far as the other characters I've got? One wouldn't care, another would be happy, and the last would...well... I guess it depends on what you call 'faction'. Does a player-created faction still count as a faction? Because if that went, and it was the sole reason that the character existed, then yeah, I think they'd have a hard time surviving on their own.