Mr LostmanActually, if you are a priest, you are almost assuredly atheist. Priests who exhibit real faith are dangerous to the organization, and tend to be sent as “missioners” to some faroff country. Or as Ramses from Anne Rice's Ramses the mummy put it: “I was called a god all my life so I know better than anyone that there's no such thing as gods”.
Far be it from me to generalize about the average commoner and their beliefs, but I'm sure the elite were all religious. Where else did they get that “Divine Right” thing that's important to their power?
As for when humans go extinct… Because we will become extinct, nothing is eternal. Entropy, anyone? Ahem, when humans extinguish, we aren't going silently. Do you think we are going to hand over the world to the next-most-suitable species? Or that they are going to wait patiently until we've left the building to start making tools and taking over? No, it is war! The only rule of nature is that living equals killing. Sure, it is easy to be all full of yourself and mock those who smack baby seals with a club, but when it comes to choose whether you and your children or the beautiful Monarch Butterfly gets to live, each and everyone of us would torch the Monarchs and dance on their burning piles of corpses. So, as our time is running out, we'll start dragging more and more species into the destruction, so that we can win that extra couple of decades. It is only natural, despite what you would like to think it is not against any sane moral, and each and every species would do it if… No, each and every living being does the exact same thing, only not so well as us.
So, when the last human has expired his/her (most likely her) last breath, the world will have only bacteriae and small insects that we didn't care about. It will be a matter of whether the Sun still has enough juice to keep Earth alive long enough for another sentient species to evolve and “take over”.