“The unremembered, ancestral crime” refers to the murder committed by Cain against his brother Abel, in the Judeo-Christian view refered in the Genesis in the Bible.
Can be interpreted both as the crime against another person (brother in humankind) as well as an interpretation of the evil of jealousy, among equals.
The Beowulf manuscript has according to some authors, its origins in pagan folklore which were unified by a Cristian copyist, who “imprinted” his view and related ancient thoughts to the dominant religious influence at the time: the Judeo-Christian perspective.
reference
Fulk, R. D. (Ed.). (2010). The Beowulf Manuscript (Vol. 3). Harvard University Press.