I don’t see how freedom of speech is relevant to that case.
Many states have statutes that prevent people from being fired for their political affiliations because that seems like a good law to have. Having a member of congress out you to your employer for being a gay, trans or a democrat is extremely skeevy and the article I found indicates it may have also been illegal (not unconstitutional, but in violation of a statute).
I don’t know if any states have laws that prevent colleges from denying people admission for posting racist stuff online. Perhaps that’s because that doesn’t seem like it violates someone’s rights.
We can actually tell the difference between bad things and not-bad things, even if we can put them into the same very broad category of “having someone tell someone something you said.” That category includes passing on the loving words of a dying person to someone who couldn’t be there, telling the police that your friend has been amassing bomb-making materials, and calling your friend’s employer three times a day to tell them about your friend’s sexual adventures. It runs the gamut from kind to morally required to violation of trust and harassment.