My answer assumes said employer is stupid enough to cite the handshake as the reason for firing the guy:
I'd say it depends on the job. If the guy is an at-will factory hand (haha) then the business should be able to make the simple accommodation of not shaking his hand, even if it is highly offensive. The guy doesn't need to shake hands to do his job. That is, if they would like to avoid a wrongful termination lawsuit, which this person could arguably bring in California under
FEHA, believe it or not.
Equal employment laws in the US generally will generally force most employers to make reasonable accommodations of religious beliefs that do not create an undue hardship on both parties. I think this is sound public policy. And US state and federal employment laws will provide avenues for employees to sue a business, even if the employee was at-will, if he can show he was fired because of his religion,
and that this religious practice could have been reasonably accommodated, but was not.
If the guy was in a position where face to face human interaction was an important part of his job, like sales, a religious accommodation would be hard to do and could be an undue hardship on the business to accommodate. Under those circumstances firing the guy is probably OK.
Obviously this sounds pretty silly, but most businesses are so paranoid about this stuff that I'd be surprised if a semi-knowledgeable boss would take the risk and can this guy outright (assuming they made the mistake of hiring him in the first place) no matter what business he was in. Practically speaking they'd be silly to cite the handshake as the reason, since it would probably not be difficult to find some other reason to fire the guy.
As to the question should the state get involved... well the state should get involved in questions of religious discrimination in the form of laws prohibiting it within reason. Like I said I think that is good public policy. This, obviously, is stretching religious accommodation within reason. I personally would not shed a tear if such a person was fired for refusing to shake a woman's hand and wound up losing his case.