Favored disciplines and clan weaknesses aren't hereditary - they're cultural.
Caitiffs are vampires who don't know what clan they belong to. They don't get favored disciplines or a clan weakness (their weakness is the social disadvantage of being clanless). The thing is, a caitiff has to belong to a clan by definition. They're ultimately descended from some bloodline or another, they just don't know which. Thus favored disciplines and clan weaknesses aren't hereditary - they're cultural. By the rules, if a vampire doesn't know his sire was a Giovanni, his bites don't hurt like his sire's do, and a Lasombra would have a reflection.
- What about Caitiff who know who their sires were and who hung out with their sires and learned all the jazz, but were still Caitiff? This can and does happen. It's not always immediately apparent, though, especially with Clans like the Brujah or Toreador who have no easy-to-determine weakness and a fairly common Discipline suite.
- It should be noted that some kindred that actually have been successfully embraced into a clan (mostly anarchs) declare themselves caitiff primarily because they see the stregths of not being tied to a clan rather than the weaknesses, even though they still have the weakness of their clan, in contrast to those embraced as caitiff (to elaborate, a human embraced by a nosferatu but ending up a caitiff due to the embrace will still look normal, whereas a nosferatu embraced normally declaring itself caitiff will still look like a walking hemmoroid). In short, there are true caitiff, kindred who truly lack the clan flaws and disciplines, and kindred who simply declared themselves caitiff or don't know their clan. And they are generally easy to tell apart, especially when that fancy-dressed hungry caitiff simply can't bring himself to feed on that hobo across the street despite how much he wants to and needs to.