You must be reading a different article. Nugent doesn’t state that McCartney doesn’t have the right to fire whoever he wants.
What Nugent says is “Neither I, nor any hunter or meat eater on the planet, has any desire whatsoever to influence any vegetarian’s choice of diet or to force them to eat meat. We are the friendly, tolerant Americans.
This is but one of many issues that represent the line drawn in the sand between liberals and conservatives.”
So Nugent is pointing out the hypocrisy of the left and how intolerant they are.
His points about liberal intolerance are mostly good ones, but I think by butting into somone's private matters this way, not to mention boasting about his food preferences and ridiculing someone elses, he's doing just what he's complaining about.