People would likely collectively go "Huh. Who saw that coming?"
Then, likely you'd see most of humanity adhere to said religion. This is nothing new. Humans tend to clump together over all sorts of group gatherings. When Team X wins the super bowl, suddenly Team X gains a whole lot of new fans.
I do agree with some of the others (as well as yourself) that this is an impossibility, however. Religion as we know it today is strictly un-provable. It's built in to the definition of what constitutes religion today. Even within the major religious movements, there is so much fractured history that there's no one real story of any particular god.
That said, if you're looking for examples of what the existence of a real god might end up looking like, you can find those in a lot of the major religion's texts. 332
The Bible, for example, is based on the assumption that God is real and does real things.
UPDATE:
After pondering this more and reading through the other answers (which are all interesting...even if I don't agree with them all) I think there's perhaps even a higher-level answer to this question:
It all depends on what particular god was proven to be real and that god's particular rules of the universe
Someone brought up reincarnation and I think that's an excellent example of but one particular aspect of religion (the afterlife) that could have drastically different effects on society depending on which version 'proves' to be real. Are you reincarnated as an animal? Do you go to Heaven? Hell? Is heaven the greatest thing ever?
All sorts of scenarios could stem from that:
* maybe the afterlife is 'pretty good' in that for a good chunk of the planet's population, they decide death is the next logical step. That could be good (planet's population under control)? Or bad in that whenever life just gets too hard, people just kill themselves (endless cycle of depopulation)?
* maybe it's a gamble. Heaven or Hell. Maybe then there's a sudden wave of empathy and sympathy and governments start shifting towards more socialist and communal models and everyone starts striving to better humanity. That could lead to an interesting 'utopia on earth' model (hmm...there's a story idea right there...)
* maybe heaven is a non-stop orgy and all-you-can-eat buffet. Within the weekend humanity no longer exists. Win win for everything as humans are partying in Heaven and the Rhinos and Elephants back on earth can finally do as they please.
* maybe it's "There is no afterlife, this is all you get" in which case maybe not a lot changes at all...some societies are OK with this now and live peacefully, some societies are everyone-for-themselves and that wouldn't change either. 590