“…and you shall be to me a kingdom of priests and a holy nation. … And also let the priests who come near to the Lord consecrate themselves, lest the Lord break out upon them.”
Short answer
The Church agrees that all the baptized are a holy priesthood. She also teaches that there is an ordained priesthood, which differs from the common priesthood in essence and exists to serve it. Israel was likewise called a kingdom of priests and still had priests set apart within it. Augustine calls all believers priests and in the same sentence speaks of bishops and presbyters as priests in a special sense.
Drafted from primary sources. Every quotation is checked against the page it links to.
Where this teaching appears on the Offshoots timelines: August 1520, No ordained priesthood apart from all believers.
16 quotations in date order
“…and said to them, "You have gone too far! For all the congregation are holy, every one of them, and the Lord is among them; why then do you exalt yourselves above the assembly of the Lord?" … And Moses said to Korah, "Hear now, you sons of Levi: is it too small a thing for you that the God of Israel has separated you from the congregation of Israel, to bring you near to himself, to do service in the tabernacle of the Lord … And would you seek the priesthood also?”
“…because of the grace given me by God to be a minister of Christ Jesus to the Gentiles in the priestly service of the gospel of God, so that the offering of the Gentiles may be acceptable, sanctified by the Holy Spirit.”
“…and like living stones be yourselves built into a spiritual house, to be a holy priesthood, to offer spiritual sacrifices acceptable to God through Jesus Christ. … But you are a chosen race, a royal priesthood, a holy nation, God's own people”
“So I exhort the elders among you, as a fellow elder and a witness of the sufferings of Christ as well as a partaker in the glory that is to be revealed. Tend the flock of God that is your charge”
“Woe to them! For they walk in the way of Cain, and abandon themselves for the sake of gain to Balaam's error, and perish in Korah's rebellion.”
“For his own peculiar services are assigned to the high priest, and their own proper place is prescribed to the priests, and their own special ministrations devolve on the Levites. The layman is bound by the laws that pertain to laymen.”
“In like manner, let all reverence the deacons as an appointment of Jesus Christ, and the bishop as Jesus Christ, who is the Son of the Father, and the presbyters as the sanhedrim of God, and assembly of the apostles. Apart from these, there is no Church.”
“And so it comes to pass that today one man is their bishop, tomorrow another; today he is a deacon who tomorrow is a reader; today he is a presbyter who tomorrow is a layman. For even on laymen do they impose the functions of priesthood.”
“Thus Korah, Dathan, and Abiram, who endeavoured to claim to themselves the power of sacrificing in opposition to Moses and Aaron the priest, underwent immediate punishment for their attempts.”
“…but they shall be priests of God and Christ, and shall reign with Him a thousand years; and this refers not to the bishops alone, and presbyters, who are now specially called priests in the Church; but as we call all believers Christians on account of the mystical chrism, so we call all priests because they are members of the one Priest.”
“…those men are received by the Church as its rulers whom the Holy Ghost prepares: so that in the people of God's adoption, the whole body of which is priestly and royal, it is not the prerogative of earthly origin which obtains the unction, but the condescension of Divine grace which creates the bishop.”
“A devout layman is united with Christ by spiritual union through faith and charity, but not by sacramental power: consequently he has a spiritual priesthood for offering spiritual sacrifices … Hence, too, it is written (1 Peter 2:5): "A holy priesthood, to offer up spiritual sacrifices."”
“And if anyone should assert that all Christians without distinction are priests of the New Testament, or that they are all inter se endowed with an equal spiritual power, he seems to do nothing else than derange the ecclesiastical hierarchy … as if, contrary to the teaching of St. Paul, all are apostles, all prophets, all evangelists, all pastors, all doctors.”
“Christ the Lord, High Priest taken from among men, made the new people "a kingdom and priests to God the Father". … Though they differ from one another in essence and not only in degree, the common priesthood of the faithful and the ministerial or hierarchical priesthood are nonetheless interrelated: each of them in its own special way is a participation in the one priesthood of Christ.”
“The whole community of believers is, as such, priestly. … While the common priesthood of the faithful is exercised by the unfolding of baptismal grace, a life of faith, hope, and charity, a life according to the Spirit, the ministerial priesthood is at the service of the common priesthood.”