How is the future breakdown of Anglo-Saxon society portrayed in Beowulf?
In Beowulf, there are pagan themes as well as Christian themes. Therefore, Anglo-Saxon society, as it is presented here, was in a transition period in terms of folklore and religious culture. Most Anglo-Saxons converted to Christianity but they kept their older stories alive and Beowulf was one of them.
Beowulf does not really represent the "breakdown" of Anglo-Saxon culture. Rather, it shows how the older culture and the new influence of Christianity were, for a time, blended as the new slowly replaced the old. One of the bigger changes not represented in the text itself was that Christianity would become a literary as well as oral culture whereas the older Germanic tribes tended to be strictly oral. A literate culture or set of beliefs can be more easily and quickly spread than an oral culture can.
Most scholars say that Beowulf was written by an Anglo-Saxon Christian sometime between the 8th and 10th centuries. And he wrote it about a Scandinavian hero (Beowulf) who would have lived sometime in the 6th century when the culture was pagan. So, in the story, we see some Christian themes placed on top of the pagan and more ancient Anglo-Saxon themes that would have been characteristic of that older era.
One of the ways we see this is that Grendel is described as a descendant of Cain, a character from the Old Testament. The Old English term "wyrd" which means fate, seems to be interchangeable with a notion like God's will. There is also a reference to the Flood in Grendel's mother's lair. So, we can see the encroaching influence of Christianity, but the anonymous author stayed true to, or clung to, the older pagan motifs.
If there is any evidence of a breakdown in the 6th century Anglo-Saxon culture, it is the constant feuding between tribes. However, this is not explicitly replaced or roundly condemned in Beowulf and it had been going on for some time. The main shift in Beowulf, in terms of culture, is the transition from pagan to Christian society.