"Tonsure" derives from a Latin word meaning a shearing or shaving. It refers to the part of a priest's or monk's head that is shaved, often just prior to taking holy orders. Like the “ungirdled" dressinggown, Mulligan’s “untonsured hair" suggests lack of reverence for the rite he is imitating, and for the Catholic religion in general.

JH 2011

Source: www.newliturgicalmovement.org.