In other words, he publicly harassed a colleague who (for what could be any number of perfectly valid reasons) preferred not to publicly state their beliefs. That would seem to me to be an eminently reasonable reason to fire someone. If you go around publicly harassing your colleagues to publicly state their political opinions, you deserve to be fired.
If staying silent is unacceptable and saying something "wrong" is unacceptable, then it's in your own self interest to learn the "acceptable views" (whether you agree or not) and mouth them whenever the Powers that Be demand it.
That's quite twisted.
Free speech isn't the First Amendment. Free speech is a broad foundational principle of liberalism, and the First Amendment is just an encoding of this principle in the context of the U.S. government. But go back to Mill's "On Liberty" and you'll find that he was just as concerned about threats to free speech stemming from social disapprobation as those from the government.
Anyway, I prefer this modified version of the strip: https://pbs.twimg.com/media/ECqxDQGVAAAXUgK?format=jpg&name=...