You're missing the fact that he lost his job because of the pressure of GLAAD for saying what he believed in.
He was NOT in A&E's "house" when he stated his religious beliefs.
Your analogy is absurd.
Earlier this year, a number of contestants in the reality show "Big Brother" made several clearly bigoted and racist remarks about other members of the cast.
They were fired from their real-life jobs before the show ended because the companies that they worked for did not wish them to be associated with their companies.
That's an employer's right, and that is A&E's right as the network that airs Duck Dynasty. Generally speaking, we're an "at will" employment nation, and as such, an employer can fire you for a good reason, a bad reason, or no reason at all.
So things that you do outside of work can (and will) get you fired, like it or not.
If A&E did not wish to be associated with Phil Robertson as a result of his remarks, they had every right to do so.
In fact, they didn't even have to give anyone a reason why they fired him.