I think they have to do something fresh. They've done the Judeo-Christian artifacts (the two best ones). Revisiting Jewish and Christian relics is too predictable perhaps. They've already proven the power of God and of Christ in prior films so there's no question about the mystical qualities of a religious macguffin.
I think that's why they gravitated towards aliens for #4. It was a departure from the formula. The aliens and ancient pyramids connection has become popular over the past 30 years, even if it's still only perhaps 25% of the masses who believe in that stuff. It's still "mysterious" and the construction of the pyramids to this day unexplained (at least in Egypt), which is why I feel KOTCS still works as an Indy film. There is real history to it even if it's Sci-Fi.
If they were to go back and use Judeo-Christian relics then I would love an adventure about the Spear of Destiny. It was the spear used by Longinus to pierce Jesus's side during the crucifixion and became a religious weapon used in the Crusades by knights to fight Muslim invaders. The myth says that they used the spear to raise a dead army which helped them defend Jerusalem. Imagine escaped Nazi's trying to get that to rebuild their army! This is likely too close to the Grail though and why I think they go far away from standard religious objects.
I had thought they could perhaps have Indy search for a Muslim relic in a 5th film, but I doubt very much that they'd want to support or legitimize that faith given the radical terrorism and the way women are treated. Plus, who needs the backlash from fanatics! We all saw what Muslims did when there was a small cartoon depicting Muhammad and how Muslims have fire bombed churches in Malaysia recently because they use "Allah" as a reference for God too. I don't think it's worth it just to give Indy something to search for.
I think Norse mythology (Hammer of Thor, Odin's Spear) or Greek/Roman Gods (Zeus' Thunderbolt, Poseidon's Trident) could be a good angle. It may be tough to reconcile the "one true God" of Raiders with multiple pagan Gods (at least with aliens God is still likely their creator), but since they had already done voodoo and black magic in "Doom" I think it can work.
Whatever they come up with, I'll surely be very curious to see it!