However, the main criticism I've seen directed towards the author of the manifesto, is that he contributes to creating a toxic work environment where women feel less welcome, which makes it hard to keep him employed in a company that wants women to feel welcome in engineering. Also that he doesn't understand the need for diversity in modern companies, that he doesn't understand the need for empathy and interpersonal skills in engineering, and that he's wrong about many of his assertions about gender differences (many gender differences are the result of cultural bias, for example).
> I didn't say anything about literally preventing someone from expressing their views.
You said:
> many people's first instinct, when faced with views they strongly disagree with, is to try and suppress those views and the person speaking them
The views weren't suppressed, they were spread, and then criticised. No doubt there are people who want to silence people they disagree with; that is nothing new unfortunately.
Whether his firing was justified or not depends primarily on whether this manifesto indeed contributed to a toxic work environment where women feel less welcome. Many people think it did. And if it did, then it's kinda hard to Google to keep him employed.
That's really the core issue here: is his manifesto intolerant of women in engineering, and does it contribute to intolerance of women in engineering? There's a vital difference between merely expressing an unpopular opinion, and expressing intolerance towards your coworkers. He's not merely supporting an unpopular sports club or liking unpopular music, he is talking about his coworkers. And that changes everything.