As CEO your job is (a) leadership and (b) communications. He failed at both, badly. Perhaps he should have reached out to internal resources more (HR, PR, crisis PR, etc), but these are things I expect a CEO to figure out.
I'm not teaching a new hire coder what a computer is. Nor am I teaching a CEO about PR and communications!
Literally all he did was monetarily support a cause ($3,100) in private. He was not out there making statements or instituting changes to the company.
What does that have to do with "leadership and communications"?
I certainly don't align with his political position but respect people's right to hold one without fear or favour.
It has to be one of the most egregious acts of employee activism. And look where it got Mozilla now, the politically palatable replacement has driven it into the ground while it's only held afloat with money from Google.
Political donations are not private. They're a matter of public record (a point Eich himself has agreed with in interviews).
As presumed-CEO and leader, he needs to have the confidence of his organization, and also the ability to address controversial difficult topics. He failed on that.
He finally did the right thing by stepping down. He would have always carried the weight of the mismanagement of the response to the employee-criticism, and that is what killed him ultimately.
A CEO position isn't a reward, it's a service position, and I believe that no one is entitled to it. (Ditto many forms of leadership) So to complain about how unfair it was to him, perhaps we should think about how unfair it was to the employees of the organization who had to deal with situation instead.