So, do all Gods on all worlds have influence in Golarion setting? For example, in the context of Pathfinder... are there people that worship Desna, Shelyn, Erastil and such on Earth? Could someone from Earth who a cleric of the Christian faith (like a "faith healer") who ended up on Golarion... would they have to convert to a Golarion god, or would the Christian God still be able to grant them powers?
Same for the Greek and Roman and Norse gods... do all gods 'real' (by real I mean from real world religions) and 'fictional' (by fictional I mean ones made up entirely as fictional gods, not from any real world religion)
It hopefully goes without saying, but I just want to be clear, this is not intended to be a discussion of real life religious beliefs, and my mention of "faith healers" is in no way an invitation to discussion on whether they are real or not in the context of the real world I am merely wondering if there is any information on what happens when a FICTIONAL Earth/Greyhawk/Faerun worshipper (cleric or not, but especially cleric) ends up on Golarion.
I ask because some campaign settings in the past have done it one way, others have done it another way. For example, Forgotten Realms 3.5 specifically said that when a cleric travels from Greyhawk to Forgotten Realms, they are CUT OFF from their god and lose their powers until they turn to a Faerun deity. Ravenloft also had a similar thing (at least in the White Wolf writeup), although there the Dark Powers granted the clerics power and deceived them into thinking their deity was still with them.
If you're looking for "official" answers, there aren't any. I suspect that this is something intentionally left to DMs to work on their own. Golarion clerics may be maintaining their powers solely based on their faith in their distant deity as opposed to said deity actually having a presence on WW1 Earth. Use whatever interpretation you want.