I believe it would be worthwhile for you to take the time to read the single paragraph which constitutes our First Amendment.
Nowhere in that amendment, does it say that you can say anything you want with no consequences. Indeed, that would be stupid, and impossible to enforce.
What it DOES say, is that CONGRESS cannot make laws abridging the freedom of speech, or of the press.
The problem here is that employer in this instance is not a private entity, it's an office of the state. And the states are required to uphold the First Amendment just as much as the Federal government is. The man was running for elective office, his employees engaged in speech he disapproved of, and he terminated their employment as punishment. IANAL, but that looks like a clear breach of the First Amendment to me.
To repeat, not all speech is protected.
And, a reading of the Judge's memorandum, which has been earlier presented here, shows that he found that the speech in question was of a personal nature, not that of a public interest.