“The solution, then, was to devise a public-relations strategy to cast the Church ‘as a sensitive, caring entity.'”
Public relations isn’t normally hyphenated. But here it is. And it’s right.
Think of a hyphen as glue. It’s sticky. It keeps two things together. When you want to keep two words together that normally appear separately, a hyphen is what you need.
In this sentence, you need public and relations to hang together as a single adjective, modifying strategy.
If you don’t hyphenate public-relations, the meaning could easily be misconstrued: the sentence might be about a relations strategy that was public, as opposed to private.
Same deal with man-eating shark (ironically the opposite of man eating shark) and the classic dirty movie theatre (which needs cleaned up, but not because of the porn).
And let’s not talk about the father-to-be stabbed in the back, which already happened — as opposed to the father to be stabbed in the back, which is still being planned.
(Hyphens are connectors. Now dashes — dashes are dividers. Hyphens are little, dashes are big. When you want to make a big break between words, phrases, or ideas — well, look here — I’ve just interrupted myself — a dash is the perfect interrupter. Don’t ever use a hyphen as an interrupter-it isn’t appropriate-it connects things you wanted to divide-and makes you look like you don’t understand the difference between little and big. Size matters.)