You don't actually "need evidence of bias". You can let someone go if they are not an asset to the company. This guy certainly wasn't once the amount of annoyance and upset his words had caused others in the company was pointed out to management.
It's always lovely to see people who, I'm sure, are staunch defenders of "workers rights" turn around and say "yeah just fire anyone who isn't currently an asset to the company by whatever criterion".
The difference between "can" and "should" is the entire moral universe.
