There's no "free speech" at work [-places] in the USA. That's not what free speech means anyways. You can and will be absolutely be fired for saying things at work that are incompatible with your employer's opinions. I can't think of a faster way to get fired anywhere than insulting the person running the company you work for, private or public company, definitely in public.
The US has less free speech than some other countries. Especially now, but this was always true at corporations. In the US you can be fired for anything, including speech.