I'm a christian. (waits to get attacked by atheists) Jk JK don't hurt me! (except for the chrisitain part but I don't give a damn about what other people beliefs are so..)
Now to bring this back on topic there is an explanation on why people could still believe religion in Fallout. Maybe there is a cult somewhere that thinks that God or whoever respective religion they believe in let it happened because of Humanity's sin. Also in the Bible they did mention that there would be a battle between humanity in a God forsaken wasteland. (See what I did there?
) correct if i'm wrong because I only read a few chapters in the bible. (I may be Christian but i'm not that into it.)
Now onto the major religions. Islam in my opinion will definitively have some survivors. After all there are over 2 billion of them in the real world. That is unless Islam died out quick in the Fallout Universe. We also may have Hinduism, though you may have a better chance at finding them in India/ Southeastern Asian countries. The same applies for Buddhism. I doubt Judaism will make it since it's a small religion and most of the followers are in Israel which might have gotten nuked by Muslim countries in the great war. (after all both religions hated eachother)
For the smaller religions chances are do to their small numbers they may have gotten blown up by the nukes and the survivors dieing of in the wasteland. Now If you disagree with what I said you can kindly post a reply pointing it out.