The Catholic Encyclopeida article for "Beard' suggests that they have been a number or variations over time about whether it is permitted for clergy to have facial hair. the general consensus is that in the Eastern Orthodox tradition, being beardless was a sign of effeminacy, so priests and monks generally wore beards as a sign of their role as male authority figures. In contrast, the current western tradition for catholic priests to be clean-shaven seems to have arisen out of a desire to distinguish themselves from military men who often cultivated elaborate mustaches. However, a review of contemporary portraits of Catholic clergy suggests that this dictum was not enforced with any stringency prior to the mid-18th century, at least for the secular clergy (that is, the regular parish priests -- monks and nuns have their own set of rule depending on which order they belong to).