I don't see the difference. I don't trust either of them to do their jobs properly if their mental model of reality is based on religion.
And you consider that rational? Do I care if my car mechanic believes in ghosts? Why would it matter? Because it might mean he could have other strange ideas as well? How about I cross that bridge when I get to it and first meet the person, and maybe start caring about their beliefs once they actually do fuck up, instead of plastering my beliefs about their beliefs, and how it influences their work, all over it and calling it a day? At any rate, I would sooner look out for their office being littered with gifts from pharma salesmen and ads, if you catch my drift, and you can worry about bogeymen in the meantime.