The inherent issue is the clause of "posting things contrary to the best interests of the university," which is extremely open-ended language as "best interests of the university" is not defined. If you want to fire a professor at KU for basically acting like a dumbass during a mass shooting, that's one thing, but "best interests of the university" could be construed to mean so many different things that there needs to be additional language delineating exactly what that phrase means. Given that Brownback has shown himself to be extraordinarily petty in the face of criticism (remember the high school kid who insulted him on twitter), is it that outrageous to think that he might personally intervene with his own appointed regents in the case of a professor who publishes research or critcism of Brownback on social media that he doesn't want to see the light of day?
The potential for abuse is more likely at a lower and more petty level but this policy is so broad that even the more off-the-wall scenarios could happen at this point.