In addition to everything pseudalopex said below, which I agree with 100%, I'll just add that, yes, some things absolutely are and should be black-and-white, my-way-or-the-highway. Particularly, issues of human- and civil-rights.

The opposition to Eich was not because of some unpopular opinion he held at some vague point in the past. He wanted to ban same-sex marriage in 2008, and all indications are he still wanted that in 2014. Eich had ample chance to easily diffuse the situation by clarifying his beliefs; instead, he provided vague platitudes about inclusiveness and leaving his personal opinions at the door.

I'm sure there's plenty of companies that wouldn't mind having an anti-gay-marriage CEO. Hell, most people could stomach working with someone with those views; remember Eich was chief technologist and a Mozilla board member from the start, and CTO from 2005, which Mozilla's LGBTQ employees obviously tolerated. But I'm sorry, I have very little trust that a company can maintain a certain set of values, when I know for a fact its Chief Executive Officer holds diametrically opposite views. Management shapes every aspect of a company, so the personal opinions of the person holding the highest position in that chain matter.

There is nothing unethical about acting this way. This is not denying Brendan Eich his humanity (unlike what his views do to others). Being CEO of Mozilla is not a basic human right that he is being denied.