Science, history, geography, literature, medicine, legal stuff - monks wrote about all of it. My area is early English history, so that's what I can speak to; the best example of a manuscript that covers so much more than religion from that period is the Anglo-Saxon Chronicle, which was begun during the 9th century, attempted to explain English history up to that point, and then was added to yearly until the 11th century. We also have jokes, riddles, and charms (some of them surprisingly dirty/risque) that were recorded by monks, poems (like Beowulf), medical texts (Bald's Leechbook is a cool one to look at), and texts like the Voyage of Ohthere, which was part of a larger manuscript that was translated/adapted into Old English from a Latin text, copied multiple times, and explained the topography of Norway. There's also the classic Ecclesiastical History of the English People, which is about religion and history but not strictly a religious text. I'm sure monks in other places were writing and copying the same kinds of material as the English were at the time; they're generally the reason we have any of the documents that we do for the early medieval period. (Edited to clarify the bit about where Ohthere's text is found.)