Before anyone accuses me of "being a fascist" for supporting this kind of censorship, take a moment to read the article again. He's not telling people to resign if they are pro-Trump, he's asking people who are going to actively make others' lives worse through hate-speech and derogatory action to resign. Remember that your liberties end where other's liberties begin.
Does that really need to be said? I'm sure it's already in the employee handbook that you can't call people racial epithets or sexually harass people.
Try to put yourself in the mindset of a Trump voter working st GrubHub and receiving that email. That wouldn't make you a little bit nervous? Would you really say to yourself "oh, yeah, I see what he's saying here" or would you clam up and live in fear of being outed?