I think if you act in a violently nationalist way (harming or harassing someone who is "not American enough"), or taunt legal immigrants because they "look hispanic", "look indian" etc, that is all completely reasonable grounds for firing.

In my opinion, you can identify as nationalist or favor immigration restrictions as long as you don't harm, harass, threaten, etc. someone. And I think this is what the Grubhub CEO is saying (their later statement reinforces this).

This isn't censorship of ideas, it's reinforcing a culture of empathy and goodwill at a company with those values.

Think about it this way: would you enjoy working for a company that did nothing as co-workers made fun of you for your race, disability, country of origin, or sexual orientation?