I suspect that it differs depending on the family member. I also doubt that it's as straightforward as any of the options given in the poll.
Some of them probably do believe it on the surface, while harbouring different motivations deep down (fear of being ostracized by the family and/or fear of facing any cognitive dissonance they might be experiencing, attention-whoring, sadism, etc.) -- ones which they might not even be consciously aware of holding. Others might genuinely believe, and still others could just be mean assholes, like the family patriarch.
As for Fred himself: The guy fits the bill for a cult leader to a T. He's intelligent, charismatic, antisocial and narcissistic. It's impossible to say whether or not he's bought into his own bullshit on the surface, but I've long held that his real motivations are attention, sadism, the ego-trip he gets from his family basically worshiping him, and money. He obviously gets off on hurting other people, and he's intelligent enough to have worked out a way of doing that without ending up on the wrong side of the law. Plus, he very likely realizes that emotional pain is a far more profound than any physical anguish he could inflict on someone. Long story short, the dude is a sadistic sociopath.
Seriously, read the "
Addicted to Hate" article. It's an excellent portrait of Fred Phelps and the dynamic within his family.