The Aaronic or Lesser Priesthood “is an appendage to the greater, or the Melchizedek Priesthood, and has power in administering outward ordinances.” (DC 107:14).
Recall the definition of administer is “to manage or be responsible for”.
Of the offices in the Aaronic priesthood (ignoring bishop), we know “the priest’s duty is to preach, teach, expound, exhort, and baptize, and administer the sacrament” (DC 20:46). However, “neither teachers nor deacons have authority to baptize, administer the sacrament, or lay on hands” (DC 20:58).
As such, when the deacons and teachers participate in the preparation and passing of the sacrament, they are not using any authority as they do not have authority to administer the sacrament—only priest’s have been given that.
Therefore, it is clear priesthood authority it not necessary for these actions related to the sacrament. As such, woman would be able to work with the priesthod in the sacrament by helping with these tasks. It is only custom and policty that deacons and teachers are designated that opportunity.
Let Women Prepare Sacrament 