CANONICALLY DRESSED
A canon is "an ecllesiastical law or code of laws established by a church council" says the American Heritage Dictionary. The same dictionary notes that the adjective form of the word, "canonical" means "Pertaining to, required by, or abiding by canon law." In Hawthorne's tale, the priest is evidently dressed in the habits of the Anglican Church as prescribed by canon law. This garb was offensive to the Puritans who criticized the Anglican Church for being too much like the Catholic Church in its ritual and ornamentation. Therefore, the Puritans often leveled the charge of "Popery" at the Anglicans.
The American Heritage Dictionary of the English Language 1979 ed.