But he's syndicated. The Plain Dealer doesn't "work with" him any more than I "work with" Mitchell Hashimoto, for example. Nearly all of these newspapers work through a syndication middleman that operates professionally and neither represents, nor transmits, their cartoonists personal opinions on other platforms.
Firing someone for being an asshole in the office is perfectly legitimate. Firing someone for being an asshole somewhere else that your employees have no reasonable chance of even knowing about other than through the tweets of people they don't even know is absolutely ridiculous.
This whole thing reminds me of the Yarvin / Strange Loop fiasco.
We've, as a society, decided long ago that private and professional lives are generally distinct. We accept that the alcoholic who gets shitfaced every night after work is a perfectly acceptable coworker as long as he doesn't come to work drunk. We accept that whatever crazy shit you might get up to in your bedroom has no bearing on how you comport yourself at work. But recently we've somehow made a bizarre exception for personal opinions.