Too hard for me to conclude it is unethical given the parameter of (simple) handshake. I would think the general rule in the wordplace ought to be no touching of any kind, regardless of gender (or level of authority). I imagine some jobs would have exceptions to this, but that the general rule makes most sense. Yet, handshaking is so common, I don't see that rule taking effect anytime soon.
I've had office jobs where women will touch me (and other people) in ways that men do not. Not necessarily inappropriate ways, but if going with the general rule above or the fact they men generally don't touch each other that way, and probably ought to touch women in that way, then it is possibly inappropriate. But is seemingly so natural. Like how a woman can get by with touching a man on his forearm while making a point, whereas most guys would never do that with another human.
Me, personally, I'm prone to allowing people to touch me or me touching them, thus handshaking not a problem. But as a rule for everyone, I think it better to assume it never okay. If someone broke the no touching rule, I wouldn't see that as unethical, just following the context of the workplace rules. Since we currently have loose rules around touching in the workplace, then I do think it is up to the individual. If they wish to have some people touch them and not others, that's on them, and not unethical. But given what the article is saying, it is something to address beyond religious convictions. Perhaps something to ask about during interviews?
Then, you wouldn't choose, you'd just not shake hands with anyone.