Put aside the more virtuous public universities, where such matters are governed by law. What policies should private universities have toward freedom of speech for university staff? This is not such a simple question, even if you are in non-legal realms a big believer in de facto freedom of speech practices.
Just look at companies or for that matter (non-university) non-profits. How many of them allow staff to say whatever they want, without fear of firing? What if a middle manager at General Foods went around making offensive (or perceived to be offensive) remarks about other staff members? Repeatedly, and after having been told to stop. There is a good chance that person will end up fired, even if senior management is not seeking to restrict speech or opinion per se. Other people on the staff will object, and of course some of the offensive remarks might be about them. The speech offender just won’t be able to work with a lot of the company any more. Maybe that person won’t end up fired, but would any companies restrict their policies, ex ante, to promise that person won’t be fired? Or in any way penalized, set aside, restricted from working with others or from receiving supervisory promotions, and so on?