The Blinding Ritual and the Demon Tag Ritual are performed by the Himuro family master. The master wears a mask when he performs the ritual. This is probably to eliminate the maiden of all worldly connections.
All participants of the ritual are family members. Meaning, "The one who is sacrificed and the one who performs the sacrifice" may be directly related.
My theory is that the mask serves to eliminate the maiden's attachment toward her family. Gouging out the eyes of the demon in the Blind Demon Ritual may have similar meaning.