E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
To quarrel over the bishops copeover something which cannot possibly do you any good; over goats wool. This is a French expression. The newly-appointed Bishop of Bruges entered the town in his cope, which he gave to the people; and the people, to part it among themselves, tore it to shreds, each taking a piece.