Feuds are mentioned throughout the epic tale of Beowulf. When Hrothgar is telling his men how he knows of Beowulf's father, a feud is mentioned. Even in the closing of the epic, one person mentions the fear of the feuds returning now that Beowulf is gone.
The importance of the constant reminders of feuds in the epic parallel the idea that evil was always around the corner. This tends to make sense given if one is not with another, they are against them. This was also a time of turmoil. Clans were out to prove who was the most powerful. Religion was being changed (from Pagan to Christian). Too many new things were coming about. While some people were not willing to change, others could not help but try to impress upon them the "rightness" of their own ideas.
Another thing is the idea of the feud. Feuds were not new things. They existed for many years. The fact that story-tellers could use old feuds to show the meaning behind something also made Beowulf a sort of moral epic as well. This said, the greatest feud mentioned in the epic is that of God verses the Devil (a feud which surpasses all others).