Is she asking them to fire people for being sexually unattractive?
Sort of like the difference between "white people" and "white supremacists". Except that currently we don't have separate (reasonably brief) terms for the above categories.
There's nothing wrong with having employees who are unattractive / can't find sexual partners, and I agree that that would be just as ridiculous a criterion to fire someone over as being caucasian. However, if you have people in your company who are filled with vitriol or considering violence (be it because they hate women who won't sleep with them or because they hate people with a different skin color), that's a problem waiting to happen.
I personally find "people who hate people with a different skin colour" and "people who hate women" to be repulsive. I'd prefer not to work with those people, if possible. But I accept that in a free society, I might have to. I have no special right to be protected from opinions I don't like, and nor should I.
Nobody should be excluded from employment because of an opinion. And in a free society, it should never be illegal to state an opinion.
We are crossing the line into thought crime here, and it's frightening to see powerful people like Ellen Pao being ok with that.
My starting point is I don't think what you say or do outside the workplace should have bearing on your employment. Lots of people have bad, crazy ideas that don't significantly affect their performance.
On an unrelated note: the "firing" time hasn't arrived yet, but not being hired just because you're Caucasian isn't that uncommon nowadays.
Incel means "someone who is a member of a group who have a pathological hatred of women and men who have sex with women, who think that they have a right to demand sex, and that if it's not provided they have a right to take it by force by rape". Pao is talking about this group.
Sure these communities are incredibly toxic, but I don't think it's fair to say that every member of them has all of the beliefs you describe. Most of these people are probably mentally ill, they need compassion and empathy, not to be purged from society.
How much more bitter and angry are they going to be if they start to feel like they're also excluded from having a job?