I said "can". Not certainly. I've had games where I eliminated the Pariah and I'm buddy buds with everyone else.
This is one of the things I find most frustrating about Deity. Diplomacy is so key, and it usually comes down to luck. Sometimes you need to attack someone, and there's no way to avoid massive diplo hits, so you end up screwed for the rest of the game. Sometimes, everyone just loves you for it. Thanks, massively random factor that kicks in after 100+ turns.
In my current game, I ended up on a continent with Dido and Arabia. (As Bismarck. Blah, but I want the Master of The Universe achievement)
So, I park my second city right next to Dido's capital, trying to piss her off, and she just wants to be friends! Ok, weird, but fine. Grudgingly I accept, mostly because I know Harun is going to build Petra, and I want it. I would have attacked him first anyway, but there's a massive jungle right up to his capital, whereas Dido's capital area is mostly plains, and her tile expansion went *away from me* and has 3 unguarded hills in the 2nd tier on my side. In other words, I could have dropped 3 catapults onto that ring of hills in the same turn I DOW'd. Right. Easy pickins.
But, she wants to be friends and Harun just built Petra, so everyone turn around and march through the jungle. Time for the landsknecht blitzkrieg! I get there, DoW him, take heavy losses, but my slow, steady stream of landsknecht can't be stopped. (They cost like 70 faith lol, I was popping out one every 3 turns just from that)
I take his capital, and he offers me marble and money to stop. Why not, I need to replace some catapults. I denounce him, hit Next Turn, and lo and behold, Dido says "I share your conviction that Harun is an asshat."
She denounces him too! Then two turns later, she asks me to DoW him! I ask for ten turns, finish restocking, etc., and we tag team his new capital. (Which just built Macchu Pichu, and I of course get the killing blow)
So, wars over, Harun is history, along with his annoying religion, and no one from off the continent has met us yet. Dido loves me. Which makes me feel a little bad, because she's totally next. By the time anyone gets to our continent, I'll be the only one left.
The point is, this was so randomly favorable to me. Yes, I made some good choices, like combining Holy Warriors with Landsknecht for a zergling rush, but ultimately it was sheer luck that there were no diplomatic repercussions to slow me down or screw me for the rest of the game. I've had so many games go south because of being backed into a diplomatic corner!