FYI: You are responding to a troll.

It's certainly illegal to fire someone over that opinion, yes.

It depends entirely on his contract - I'd expect most CEOs to have a clause about their conduct causing harm to the organisation. Even if not, it's legal to convince someone to leave, which is what usually happens in public embarrassment cases.

It's illegal to discriminate against someone on the basis of their political stance. Nothing you can say will ever change that.

If that were true, no congressperson could ever staff an office. Or a campaign.

If a Republican wanted to work for a Democrat, and if he were denied employment for that reason alone, that would be illegal, yes.

I don't know where you're getting this idea from, but you really should check your sources.

There is a limited prohibition against screening for political affiliations enforced by the Federal government when filling certain civil service positions, but that's about it.

For a good summary of what types of discrimination can and cannot trigger legal liability, see here:

http://www.eeoc.gov/facts/qanda.html

No it's not. Indeed, you run a legal risk in NOT firing such a person given that keeping them around (especially in a senior position) creates a demonstrably hostile work environment.