Diversity for what purpose? They should hire whoever is most qualified to do the job, no matter what race, gender, creed, sexual orientation etc.
The issue is that today businesses want to be diverse for diversity sake -- as in, they don't want to be painted as racists because most of their team are white males. That is ridiculous. If there aren't enough women engineers at your studio, that is a question for the sociologists and philosophers not your HR department.
I do see Unknown Worlds point that by having a prominent critic in the media of certain beliefs (say, Islam) they could be closing doors of competent, exceptional potential employees that happen to be followers of Islam who may now see Unknown Worlds as a hostile environment for them. That's normal for businesses these days, but I think is problematic. If Chylinski is using the workplace (and I mean the actual workplace, not Twitter or personal social media accounts) as a podium or forum to discuss political beliefs, then that is unacceptable. But it is part of life to have your own views and be able to work with others with different views. A Muslim should not be turned off from working at a company because there are non-Muslims, or people there who are critical of Islam. For one, just because that person may be critical of your beliefs does not mean he may be someone problematic to work with in a professional, workplace environment. One may assume he may show bias against you, but we have to give people the benefit of the doubt. To suggest that a Muslim can't work in a workplace because there are individuals there who have private views that are opposite to their own is an insult to that Muslim. People do that everyday already. How many Christians have to work in a workplace with atheists? Or blacks in workplace with predominantly white people?
TL;DR - It still appears that Chylinski was fired because of his personal views expressed outside the company was making a segment of people online uncomfortable. In an ideal world, people would be able to express their opinions openly and not fear that someone will alert their employer. "I don't agree with that person's opinion on an issue they expressed outside the workplace that has nothing to do with the workplace" is NOT a justification to be fired, in my opinion. BUT, in a capitalistic system the company is there to make money. Anything to cause negative light on the company that could make it difficult to make money is a problem. Under that premise, I can understand why they fired him and why employees should not speak openly about their views in a public forum. And that is why this issue is an issue in the first place.
Actually, I would argue that the problem here is that people still think of social media as "outside the workplace" and "it has nothing to do with the workplace." THAT is the problem. People have not made the switch to thinking that social media essentially makes the world a giant "workplace" in some sense. Anything you put on there can be seen by anyone, including the people you work or do business with. You may only have a bunch of white dudes at your job, but what if you want to do business with someone who isn't? Because of social media, the non-white person now has doubts about you and your business and may choose to go somewhere else.
Congrats, you just lost money because John Dumbass couldn't resist posting his hot-take on where women truly belong in the workplace. We keep acting like this is some Einstein-level rocket science when this problem is quite easily solved:
1. Don't be a bigot (ideal)
2. If you can't not be a bigot, keep your bigoted shit to yourself and don't put it on social media
For some GODDAMN reason, certain people have real trouble not being stupid and instead want to cry "muh freeduhms" because they got fired. No. Shut the fuck up.