No, this one is unreasonable. It's this weird narcissistic thing that people do where they define a person's identity by how that person feels about them.
Just because I hate you doesn't mean I'm a hater. I also like things, just not you. Just because I'm unhappy with you doesn't mean that I am not happy, it means I'm not happy with you.
More broadly, you seem to be saying that the only reason anyone is skeptical of the Google protestors is that that the protestors don't like that person. That's quite an assumption. In reality, people simply disagree about things. And there's room for reasonable disagreement.
The difference is that once you establish that it's "defining someone's identity", then disagreement with that person is "denying their right to exist", and so basically violence, from which the person you disagreed with deserve protection. These are the lines along which this kind of conversations typically proceeded inside Google.
Hyperbole doesn't even begin to describe this.
The tech echo-chamber is fostering unrealistic opinions about life and liberty.
In your example, the co-worker may be "your disagreeable co-worker" (definition), or they might simply be "your agreeable co-worker" who momentarily disagrees with you or your ideas.
If your opinion about someone is right enough, often enough, that it serves as a workable summary of that person, that (ideally) a lot of people agree on, who have no vested interest in agreeing, then you could start to be objectively convinced there was no difference between your opinion of that person, and the definition of that person. But no simple definition of a person is ever going to capture the whole story - people are too complex.