If you do research, I think you’ll find a lot of “Mission” aviation is devoted to transporting NGO officials for work ranging from medical missions to wildlife conservation and environmental efforts.

Why?
I’d guess in many, many places, missions provide the only on demand air service.

I have some acquaintances in the Mission Aviation field, and from what I understand, it’s not quite as religiously dogmatic as you seem to believe.
I’ve been told that many try to win friends by doing good works, in other words setting an example, as opposed to “Dropping Bibles”…the “hard sell” you seem to think they all adhere to.

There are MANY mission aviation groups, and each probably has a different approach to their work. As with most things, it would probably be wise not to make too many generalizations about the group as a whole.