I have never taken "free speech" to mean "in all places, all the time," so I don't see a conflict. The public sphere (irl and on the internet) is where people are advocating for free speech. A private company's internal email list does not qualify.
I don't understand why so many people have a hard time understanding this even though it has been repeated like a million times at this point. Are these people illiterate or using some kind of TSLAQ block list like in Twitter, because they're afraid of seeing any dissenting opinions?
I'm going to go out on a limb here but I think most most people acting in good faith understand the difference between the public sphere and their place of employment with regard to free speech.
For example: if these employees had been other employees (or Musk himself) people racial slurs I think that's reason to fire them but I don't think it's reason to excise them from the public discourse.
Why do you believe that?