Immunity from whom and from what? From being sued for defamation? Sure. From being fired by his employer, a private business? No.
Yes, I should have been more precise.
The point was that a political commentator making remarks about a public figure/politician enjoys some sort of First Amendment protection, where a public figure commenting on an individual or a group of individuals does not. So while the First Amendment was present in the Bashir case, even in a casual way, there was no First Amendment issue in the Robertson case.
I found it telling that Bashir "resigned" rather than being fired, and the comments that I've read tended to be supportive of the idea that MSNBC "herded" (for lack of a better word) Bashir toward resignation under advise of counsel. Better to face no litigation at all than litigation that you can win.
That was however simply lawyers speculating.