Keep in mind that many priests are married and some are women. Not all priests are Roman Catholic. I’ve had dinner with my priest and his wife many times.
If it’s a friend who just happens to be a priest, sure. But if I’m having a priest over just to have a priest over, no. I wouldn’t trust myself to be as respectful as I should to my guest.
IME, many RC priests prefer not to be unaccompanied in the presence of women. For that reason, when I invite my volunteer coordinator to dinner, I invite others as well. It’s all about avoiding the appearance of hanky-panky.
What? As if anyone would believe a RC Priest would molest a grown woman!
:rolleyes:
Can I pick a fictional priest? If so, Father Ted might be fun. Maybe Father Dougal. But not Father Jack–I’d have to lock up the Toilet Duck, and I wouldn’t trust him not to do inappropriate things to the roast. 
Or you could go for our own Friar Ted, although friars are laypeople and he’s not fictional. 
Father-in-law is a Methodist minister (though retired now), so a sort of inevitable “yes”.