|The creator of this image doesn't get it.|
Robertson has all the rights in the world to believe and say what he wants about LGBT folks. Nobody can take that right away from him. However, his employer, A&E, has no obligation whatsoever to pay him for making comments which they feel are not aligned with their values. They are in no way compelled to continue to provide a forum for a guy who has offended a significant number of their viewers.
I imagine if an employee of Fox News (or any other network) made comments on or off the air that equated Christians with swine, that individual would be suspended. And I imagine that the same people who are backing Robertson and boycotting A&E, would applaud the suspension of this employee. And if he were to remain, I assume they would boycott the Network.
You have the right to say whatever crazy, hurtful, or morally dubious thing you want (short of hate speech, which is not protected). You don't, however, have the right to keep your TV job after you say it.