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.