This is more of an opinion about what is best for Mozilla's image in the public eye, not about anyone's right to have a job.
You can without a doubt hire a murderer as your CEO. It will always be my opinion that you should at least think very hard about doing so before you make the final decision.
If you run for president and you're a satan worshipper, then it would be my opinion that you will lose. If you own a cookie company and want to hire a murderer as a CEO, it would simply be my opinion that you may lose sales. If you don't care about my opinion, or don't care about sales, and go ahead and hire a murderer as CEO, then that's perfectly fine. At the end of the day, it's really up to you.
But if someone out there wants to organize a boycott because the CEO isn't a vegan, that's also fine.
Is HN [amongst others] calling for all people who disagree with legislation on homosexual relationships being called marriage to forfeit their rights to employment; or perhaps all those that consider homosexual sexual activity to be wrong? That seems like the logical conclusion here.
Is this going to be continued with all beliefs - ousting those that disprove of drunkennes or drug taking or polygamy or adultery?
Why should a company pry in to an employee's private beliefs and associations in the way you're suggesting?