ZD,
We assume people to be Jewish based on chazakah; a family known to be Jewish is assumed to actually be Jewish. Tat presumption, though, becomes suspect when there are known factors to question it. We no longer assume, unfortunately, that someone coming from non-Orthodox movements is definitely Jewish, because they define Jewishness differently than we do. I would think that this includes the Karaites too, unless, as daniela implies, we still assume that the majority are halachically Jewish, and any specific indivial is presumed to be from the majority.