Butt-hurt is the Right's fallback position for everything.
They live to be victims. Victims of a "war on christmas" or "violation of religious liberty" everytime someone says, "Happy Holidays". If someone asks a right-wing political candidate what they read, it becomes a "gotcha" question. If gays are allowed to marry, it becomes an "attack on the institution of marriage" as if two women going to city hall and getting a license is going to cause wives to start running out on their husbands.
There was a story this week on a "parody news" website about a schoolkid who was suspended because he wished his atheist teacher merry christmas. Of course, it wasn't true, but that didn't stop the Top Conservatives on Twitter from howling in outrage and death threats from pouring into the fictional teacher.
This imagined victimization has been cultivated by the Right for decades. Nobody should be surprised that it's been so effective on the knuckleheads.
And by the way, I am so proud that I have no idea what a "Duck Dynasty" is. I must be getting really old when I celebrate every instance of a new cultural phenomenon of which I am blissfully unaware.