Sure.
The issue is that you’re implicitly trying to find a way to say that these people’s speech should be protected, while the free association rights of their bosses and colleagues should not be. There is no principled way to consider racist trolling free speech, but not also those calling for their firing to also be considered free speech.
I think Popehat says this best.
> Private consequences are something else. Speech is designed to invoke private and social consequences, whether the speech is "venti mocha no whip, please," or "I love you," or "fuck off."1 The private and social consequences of your speech — whether they come from a barista, or your spouse, or people online, or people at whom you shout on the street — represent the free speech and freedom of association of others.
> But speech has private social consequences, and it's ridiculous to expect otherwise. Whether sincere or motivated by poseur edginess, controversial words have social consequences. Those social consequences are inseparable from the free speech and free association rights of the people imposing them. It is flatly irrational to suggest that I should be able to act like a dick without being treated like a dick by my fellow citizens
> Finally, I should note that one social consequence is employment-related. In many American jurisdictions, employment is "at will" unless the parties have a contract that says otherwise; an employer can fire an employee for any reason not prohibited by law. Private employers can generally fire private employees based on their extra-curricular speech. That's private action, not government action; it's an exercise of such free association and free speech by private entities as the law allows. Employers may face social consequences — particularly in a social media age — for exercising that right in a way that angers the public, which is in turn the public's free speech right.