The passage of course does not refer to the second century (where would the monks come from at the time?). The exact sense is unclear, the general intention is probably to prohibit unordained monks from active participation in liturgy. The prohibition is repeated in the Liber Pontificalis in the life of Boniface I, with regard to nuns. Some manuscripts also change "monachus" into "monachae" here.
The remark may be polemic to the roughly contemporary Rule of Saint Benedict, which states that when a son of nobility is offered to a monastery, his hand, together with the document, should be wrapped in the altar linen ("palla altaris"; chapter 59).