The joke is a red herring. He didn’t get fired over one joke; he got fired, it appears, for a pattern of behavior. And while I often think PC culture has gone too far, I’m a-OK with the idea that it isn’t acceptable to tell ethnic jokes in the workplace or classroom. That just seems like basic respect.
If this were the only issue, or if this professor had been tenure-track faculty, I might say that the response was disproportionate. This was an adjunct with repeated complaints over at least questionable comments. No sympathy here.