the more things change the more they stay the same. In a word, this old axiom describes how the world would react to scientific proof of GOd (or the non-existence thereof). Overall, I think if conclusive proof was to be found supporting either side, it would actually start more conflict than it would end.
If God is proven to exist - Well, the obvious question would be
which God was proven. This would only be possible if God himself/herself/themselves/itself came to Earth and told us. In which case many people will say it isn't really God after all, but either a false prophet attempting to lead them away from their Truth, or it was an alien, or some other such rationale.
However, I think the question being asked is more about scientific proof. And if it ever came to be that there was scientific proof of a Creator, then the debate begins about which religion has the right God (if any). Every religion would pounce on this discovery and use it as proof of their own beliefs. The Deists would simply sit back and say "I knew it". Most Agnostics would most probably become Deists and say, "I guess it is possible to know whether GOd exists. Oh well". Some of said Agnostics though would then conform to one religion or other.
As for the Atheists, hardcore skeptics, and other non-believers in God, some would try and claim the evidence was not conclusive or fake. They'd attempt to explain away how such evidence is impossible. They'd check the scientists credentials and history and conduct a smear campaign against them. Perhaps rubbish them for bias if the scientists involved were Theists (who knows). If they're UM users, they'd claim it was photo-shopped

. Others would act like the Agnostics, I think.
If God is proven not to exist - Like the skeptics from earlier, some religious folk would attempt to explain away the findings. They'd attempt to say that scientific knowledge is never complete, that there's evidence for GOd and we just haven't found it yet. They'd try and pick holes in the scientific studies used to prove the non-existence of God. Again, they'd conduct smear campaigns against the scientists, perhaps look at the character of the scientists who conducted the studies and claim bias if they're non-theists to start with (again, who knows). Some might say it's out of context

. Other religious people (mainly the fringe believers who don't really care and only attend their brand of belief once a week more out of habit than any real desire to follow their God) would probably continue to be exactly who they were before, except they wouldn't spend an hour a week in a church/synagogue/mosque/Temple/etc.
Deists would say "oops, my bad". Agnostics would be the same and say "I guess it can be proven (that God doesn't exist)".
Some Atheists, hardcore skeptics, and other non-believers would take the opportunity to rub it in to God-believers - "I can't believe you guys were stupid enough to buy into this mythological rubbish". Others wouldn't be so harsh.
Buddhists and Buddhism would remain largely the same, excepting perhaps the branches of the belief that hold to a belief in God.
I'm sure I've left out some beliefs and views, but overall, that is how it would work. There'd be even more conflict than before, in my humble opinion. Humanity might possibly even destroy itself over the discovery (such a defeatest, I am

).
Regards, PA