Cyrill of Alexandria
He thus designated the rest of the offering for them and instructed them to consume it, but only, as He specified, ‘in the holy place,’ and exclusively by males. (Refer to Leviticus 6:29 and similar verses.) However, the olive oil, grain, and wine, along with the redemption of the firstborn and the burnt offerings, are now to be consumed not just by males or in the holy sanctuary, but rather within the dwelling of the priest, and are available for consumption even by daughters and all close associates and family members. This distinction is essential: the remnants of the sacrifices are sanctified for the consecrated alone and should not be treated as ordinary sustenance; their designated location is indeed a sacred space.
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In contrast, the remainder, which is offered as a gift, holds a secondary significance and may be shared among the entire household of the sanctified, provided that the one partaking is in a state of purity, meaning not defiled by the law’s stipulations—such as being uncircumcised, foreign, afflicted with leprosy, or suffering from emission. Furthermore, according to the teachings of the New Testament and the convictions of the Church, this applies as long as the individual is not unholy or unfaithful, but rather devout and loving towards God. It is most appropriate for those elevated to the sacred priesthood to associate with individuals of virtuous character, filled with the love of God.