Both Uses of

consecrate
in
Moby Dick

Grace being said,—for those people have their grace as well as we—though Queequeg told me that unlike us, who at such times look downwards to our platters, they, on the contrary, copying the ducks, glance upwards to the great Giver of all feasts—Grace, I say, being said, the High Priest opens the banquet by the immemorial ceremony of the island; that is, dipping his consecrated and consecrating fingers into the bowl before the blessed beverage circulates.†
Chpt 13-15

consecrated = made holy by means of religious rites

Grace being said,—for those people have their grace as well as we—though Queequeg told me that unlike us, who at such times look downwards to our platters, they, on the contrary, copying the ducks, glance upwards to the great Giver of all feasts—Grace, I say, being said, the High Priest opens the banquet by the immemorial ceremony of the island; that is, dipping his consecrated and consecrating fingers into the bowl before the blessed beverage circulates.†
Chpt 13-15 *

Definitions:

(1) (consecrate)
make holy by means of religious rites
(2) (meaning too rare to warrant focus)
meaning too rare to warrant focus:

A comprehensive dictionary will contain less common senses of the word including "to solemnly dedicate" or to "infuse with reverence".