From the article RW linked:
Robertson credits all of his family’s success to their faith in Jesus Christ and their devotion to living a Christian lifestyle. He told CP on Thursday that his family has managed to stay humble, amid all of the fame, because they know that all blessings come from God; and in the end, everyone’s going to the same place: a six-foot hole.
“Fame is rather fleeting, as you know, or should know,” Robertson said. “Money can come and go, and fame comes and goes. Peace of mind and a relationship with God is far more important, so this is the precedent that we’ve set in our lives. The bottom line is, we all die, so Jesus is the answer. Many have told me through the years: ‘I think I’ll take my chances without Jesus.’ And I always come back and say, ‘so what chance is that?’”
Along similar lines:
Bitter Clingers Have Taken Over Your Television, or How America Learned to Stop Worrying and Love the Duck
by David Vickers
Like all great television, Duck Dynasty works because it follows a proven formula. In the case of Duck Dynasty, that formula is the roadmap to realizing the quintessential American dream. Have a clever idea. Sacrifice. Work harder than the next guy. Make it happen. Earn your wealth the old fashioned way. Pass the business and its blessings along to your children and grandchildren. Have fun. Never forget where, or what, you came from. Give thanks to God. Repeat.
Like most rednecks and hillbillies, the starring members of the Robertson clan of West Monroe, Louisiana are as clever as the proverbial old swamp fox. And so are the development execs at A&E. With Duck Dynasty they’ve struck more than ratings gold. They’ve struck a vital nerve in contemporary American culture. And I think they know exactly what they are doing.
The basic appeal for many folks, IMO, is that the Robersons are normal people who are the right kind of crazy and are funny (kind of like a real-life Beverly Hillbillies family that had the sense to stay where they fit and aren’t ignorant-naive-stupid). I also think many perceive them as an antithesis and an antidote for much in our society that has been going increasingly wrong for the last half century or so.