When a religion gets to the point of creating a monastery, a check is made for monasteries with 0 pop starting from the oldest monasteries.
Instead of just tying it directly to the monastery's age, I think it'd tell a more interesting story if it involved the rise & fall of various civs, and the spheres of the gods in question.
For instance, say two civilizations--the Sunken Oils and the Confederacy of Papers--are neighbors, and hostile to one another. The Confederacy of Papers is triumphant, and sacks/occupies most of the Sunken Oils' sites in the area. Now, both civs have gods of sun/sky/weather, and the Confederacy's sky god (let's call him Bob) wants to supplant/absorb that of the Oils (Martha), so the priests of Bob organize a crusade to "cleanse" all of Martha's (nearby) monasteries of the "heretics" currently worshiping there. The (surviving) priests of Martha flee with what movable relics they can, to any settlement of the Sunken Oils that they are able to, and from
there, check for the closest abandoned monastery. (Unless there's already a Marthan monastery still considered "safe", in which case they'd just go there.)
They move in to this strange monastery, and their "refurbishment" might take any of several forms, depending on the spheres of the gods in question & the history of their civilizations: If it was hallowed to a god with spheres totally different from Martha's, from a civ that is either now extinct or currently/formerly hostile to the Sunken Oils, then screw him, pull his statues down & toss 'em outside. But if it's yet
another sun/sky/weather god from a neutral civilization, or another deity from the Sunken Oils' pantheon, then they might arrange to
share the space: One statue venerated at
each end of the main chapel, for instance.
Meanwhile, the worshipers of Bob are conducting their own renovations, removing all traces of Martha & replacing her with Bob. It would be very flavorful if all religions had procedurally-generated
secondary traits: For instance, all temples of Bob might be rectangular in shape, while Martha prefers hexagons. So if your adventurer enters a hexagonal temple, but there are images of Bob everywhere, that would be evidence that this monastery was originally Marthan, but taken over during the Bobist Reform in the late autumn of 1024.