I think that Duck Commander and NASCAR likely share the same demographics so it is in the best business sense for them to advertise at NASDCAR events, I think that it's just free markets at work and anyone should be able to advertise wherever they want if they wish to pay for it.
While I am personally not a fan, and have issues with some of his views, I think he fits the NASCAR "culture." NASCAR likely wouldn't select someone they didn't think was appealing to the fans, and he is likely popular among many of the fans, so in that aspect, he could be seen as an appropriate sponsor.
Yes, I think the Duck Commander is a very appropriate sponsor for the NASCAR Sprint Cup. NASCAR has it's roots in the early days of southern moonshine runners. This evolved into NASCAR, which has always been a southern tradition. Who better to sponsor this traditional event than a traditional Louisiana patriarch?
It is important that we do not let our prejudices rule our life. I don't really see anything wrong about this company being a sponsor for NASCAR. I mean, what they do is legal, they pay taxes, and they harm no one. If you don't like them, well... too bad!