UW again fires professor for online porn.

He fought to keep his job on First Amendment grounds.

looks dubious

One of the exceptions to "the government cannot restrict your right to speech" is the government acting in a "government-as-employer" role. There, they can act like any other employer, and don't have special constraints just because they're the government. Employers can normally let people go because they think that they're bad for their image, and that's what the article said happened here.

...university leaders said he sullied the school’s reputation and had to go.

https://www.nyclu.org/resources/know-your-rights/speaking-out-public-employee

Different rules apply if you are making these comments in your personal time as a private individual. Generally, your statements about topics that are of general interest to the public, including current events, are protected by the First Amendment. However, a public employer in New York may discipline you if your comments either disrupted its work or have the potential to disrupt its work, including by affecting public perception of your employer if you frequently interact with members of the public in your job.

Now, I suppose you can ask whether the professor publicly releasing porn videos of himself is actually damaging to public perception of the university, but the rationale they used is a legit rationale.