So…it haz nothing to do with free speech or faith after all:

In May 2013, rumors began circulating via social media that the continuation of the show (on A&E, at least) was being threatened by “liberals and atheists” and meddling A&E officials who objected to the Robertsons’ inclusion of their religiosity (particularly in dinner prayer scenes) and the prevalent appearance of guns in the show. According to the Hollywood Reporter (THR), what’s currently holding up the renewal of Duck Dynasty for a fourth season on A&E is not a content dispute but a standoff with the Robertsons over their salary demands.

snopes.com