8 They eat up the sin of my people, and they set their heart on their iniquity.
[AD 253] Origen of Alexandria on Hosea 4:8
The text wants you to make a more daring assertion if your hearing will still follow. What is the “sacrifice” that is offered “for sin” and is “very holy” except “the only begotten Son of God,” Jesus Christ my Lord? He alone is the “sacrifice for sins,” and he is “a very holy offering.” But since it added that “the priest who offers it will eat it,” it seems to be hard to understand. For that which it says must be eaten seems to be referring to the sin, just as in another place the prophet says concerning the priests that “they will eat the sins of my people.” This also shows that the priest ought to eat the sin of the one who is offering. We frequently show from holy Scripture that Christ is also the sacrifice that is offered for the sin of the world and the priest who brings the offering.

[AD 420] Jerome on Hosea 4:8
[The priests] are feasting on the sins of my people, approving the crimes of the sinners. For when they behold them sinning, not only do they not argue but they praise and extol them, calling them fortunate.

[AD 420] Jerome on Hosea 4:7-9
"According to their abundance, so they sinned against me: I will change their glory into shame, they will eat the sins of my people, and lift up their souls to their iniquity, and it shall be as the people, so the priest, and I will visit upon him his ways, and render to him his thoughts." LXX: "According to their abundance, so they sinned against me, I will turn their glory into shame": they will eat the sins of my people, and receive them in their iniquities"; "others their souls, and it will be as the people, so also the priest, and I will take vengeance on him for his ways, and render to him his thoughts." Israel had as many altars built for demons as they had men, in whose sacrifices they sinned against me. Therefore, I will exchange their glory, in which they boasted to themselves and preferred to God, into ignominy, so that both the priests and the people may be captured. For indeed, the priests eat the sins of my people, concerning whom it is written: "Those who devour my people, like bread" (Ps 13:8). And therefore they eat the sins of my people, consenting to the crimes of wrongdoers since, when they witness them sinning, not only do they not rebuke them, but they praise and exalt them and call them blessed. About whom Isaiah speaks: "My people, who call you blessed, deceive you, and they "supplant" the paths of your feet" (Isa. III, 12). Concerning them, the Psalmist cries out: "For the sinner is praised in the desires of his soul, and the unjust is blessed" (Ps. IX, 24). Hence, both the people and the priest will equally endure the sentence of God's indignation; for not only will He visit the works that they call "ways," in which they walk, but also the thoughts which they have entertained to do such things. For not only the work, but also the contemplation of evil deeds will pay the penalty. It is easy to understand about heretics, that the more there are, the more they sin against God and glory in the people; and so they deceive the unfortunate, so that they may eat the sins of the people, and by sweet words devour the houses of widows (Luke XX). For when they see some sinning, they say: God seeks nothing else but the truth of faith, which if you keep, he does not care what you do. For by saying these things, they lift up their souls in their iniquities, so that they not only do not repent or humble themselves, but rejoice in their wicked deeds and walk with heads held high. Therefore both the people and the priest, the learned and the teachers of the law, will be equally punished.

[AD 444] Cyril of Alexandria on Hosea 4:8
They used to sacrifice goats for sin; for this reason the sacrifice was called sin. By offering a goat on the altar, the priests at the right time used to bring the intestines and the lard, and they ate the rest. This was ordered by the divine law. … “They eat the sins of my people” means they eat the offerings brought for sins.

[AD 604] Gregory the Dialogist on Hosea 4:8
But we must remember without ceasing what is written about certain ones: They shall eat the sins of my people. Why are they said to eat the sins of the people, unless because they encourage the sins of transgressors, lest they lose their temporal payments? But we also who live from the offerings of the faithful, which they offered for their sins, if we eat and remain silent, we without doubt eat their sins. Let us consider, therefore, what a crime it is before God to eat the price of sins and to do nothing against sins by preaching.