Obviously, an interviewer shouldn't reasonably hold this against a candidate, but it's in the back of their head. As a candidate, the bar to impress is made slightly higher in order to overcome that subconscious bias. One of my best friends is in this exact situation of looking to switch jobs (outside of tech, in sales) and holding a degree from UW-LAX, and he's legitimately punting his job search for a few months until this is out of the news cycle.
That's just completely unacceptable. You could be the most competent chancellor in the world, but it doesn't matter if your lifestyle choices can have that kind of negative impact on alumni. It's unbelievably selfish. If you have some inner need to publicize your sexual encounters, that's fine and well, but you owe it to the thousands of people you represent to resign from your job. The only way that I can explain this sort of blatant disregard for the impact this would have on others is that he found the risk he was taking (risk both to himself and the community he represented) to be sexually thrilling.