Incorrect. At least, it's incorrect as far as consequences levied by their employers. In the United States, government employees are protected by the First Amendment. E.G. a government department that fired employees for pro or anti gay marriage donations would mean that the government is privileging one political opinion over the other:

> the rationale now is that while government may deny employment, or any benefit for that matter, for any number of reasons, it may not deny employment or other benefits on a basis that infringes that person’s constitutionally protected interests. “For if the government could deny a benefit to a person because of his constitutionally protected speech or associations, his exercise of those freedoms would in effect be penalized and inhibited. This would allow the government to ‘produce a result which [it] could not command directly.’ . . . Such interference with constitutional rights is impermissible."

Source: https://www.law.cornell.edu/anncon/html/amdt1cfrag5_user.htm...

Edit (since HN isn't letting me respond):

> In his case, his employees exercised their right to speak, said they thought he wasn't fit to be CEO, demanded his resignation, and he resigned.

This is not entirely correct, and is omitting a substantial part of the story. The company board (who are effectively Eich's bosses) told him to step down as CEO. The CEO doesn't have have a manager and so can't really be fired like a normal employee, but the board telling him to resign is functionally the same thing.