Punishing people for speaking their minds is a fundamental idea of marxism. Even if it is for a seemingly good cause, it is still a massive violation of freedom of speech. The fact that this was even debated is absolutely terrifying. This is exactly what will eventually end America and western culture. Look up cultural marxism if you don't believe me.
While I find their misogyny repellent in the extreme, the freedom of speech applies to everyone. And it would be a bit ridiculous to fire pundits hired by a highly biased conservative network for pushing that network's views.
The great thing about free speech is that it works both ways- one has the right to it, but one does NOT have the right to be shielded from others using their free speech rights to criticize you for your speech. Let the morons be buried in an avalanche of scathing criticism for their words.
The idea that a company should fire a pundit for expressing a controversial opinion presents a myriad of challenges. Should the company have the right to fire said reporters for any reason that company chooses? Sure. But should the company feel compelled to fire pundit (which you're referring to in this case, not a reporter) for saying something that the public doesn't like -because the public doesn't like it? Not at all. By firing a pundit for their views, they loose their job for the same reason the got their job -to express (often controversial) opinions on air. Pundits will be cautious, in the future, perhaps even disingenuous in their performance in effort to keep their jobs if that precedent is set. As such, perspectives are silenced and analysis is the opportunity cost of public judgement. (Recognize also, though, that the public has every right to judge pundits as they like.)