Kevin was fired for promoting alt-right views on internal message boards at Google, and not for supporting a protest. He made several of his co-workers uncomfortable enough to report him to their managers, who gave him several warnings before rightfully terminating him as an employee.
Here's a more detailed write-up about Kevin Cernekee, what he stands for, and why no one wants to work with him (link below).
Well yes. Supporting political organisation is the form of political activity.
He was bullied and fired for these actions only, I don't see any mentions that he was annoying people any way other than expressing his views.
How is that different from penalising people for supporting violent protests?
If it's okay for you to punish for one stance and not to punish for another then you are pro-censorship. So don't be surprised when companies start to censor people you like - you allowed them to do that.