There is still "religion," in terms of improvements like temples and social policies like Piety.
I don't think it's fair to even call that "religion" anymore. If everything about religions was removed in civ4, except you could still build some temples/monasteries/cathedrals for the happiness/culture, and you could run the religious civics (without any particular religion) would we really call that religion? It isn't perfectly realistic, but some attempt at all to have religion in the game surely goes for more realism. Various scenarios and mods representing specific historical periods and events could not exist without using the religion system.
What no longer exists is a modifier that fosters alliances and antipathies in an overly deterministic way.
As for this part - I'd like anyone, whether you fully liked or fully hated civ4's religion system, to explain how it really was so deterministic and shackling. For one, the human player has almost zero requirement to ever use or care about the system if he/she does not want to. You can (and I often have) go entire games without adopting religions, or really caring too much about it in making war and allies. And at a moment's notice you can switch religions, declare war, or whatever you want for your own civ in any game.
So I really, really don't see it, especially at a level of play where a player might not just be abusing AI (if you play really low level and just convert everyone to your friend, sure, you win, but I don't think it's fair to criticize the whole system based on that). As tons of players will tell you (TMIT

) the AI is nowhere close to deterministic, religion is just one factor that might not even make enough of a difference for a large number of AI. And the system still fundamentally rewards efforts and decision making, it's not entirely random - AI themselves spam and fret over religion constantly, and a player who invests into it can have decent results.
I do know there are intentions for major changes in diplomacy, I'm just not convinced they will work out well. In my opinion, the very, very, very worst diplomatic events in civ4 were AI demands about "give us this resource" or "stop trading with so-so." I don't see how civ5 is not becoming more like this, removing religion, civic, and other obvious factors, and a few new "silly complaints" like "don't settle near us." I even think a majority of players would say this is the most annoying behavior of all from the AI, and hiding true feelings/intentions could just be worse.
I can say for sure - if we look at civ3 or previous versions, diplomacy was far and away a much worse pain than in civ4. Civ4 was by no means perfect, but it was definitely an improvement, and it was clear factors like religion and civics that helped. The major diplomatic features that players could understand and respond to = good. So I hope civ5 doesn't go entirely random and mysterious on us again. (Or the other problem being incredibly predictable AI, if the personalities are too extreme and always the same)
Also, anycent, I can't speak for anyone else and did not in fact see that on the other page before, but sorry people were being mean to you, I agree those posts were harsh, and hopefully you still find the forums a welcoming place with lots of great information and discussion.