The New Testament makes it clear that every person who is saved by Jesus Christ is a priest. We are told in 1 Peter 2:9 that “you are a royal preisthood, a holy nation.” If you read this passage inits context it is certain that this is being applied to all Christians–to all who are saved by the blood of Jesus. That all would be priests in the New Covenant was anticipated in prophecy all the way back in the Old Testament, in Exodus 19:6. “You will be a kingdom of priests and a holy nation.”
All of us who are saved are priests and we have a high priest, who is Jesus Christ. This is taught in Hebrews and elsewhere. Jesus is “a priest forever in the order of Melchizedek.” He is a high priest of a new covenant. To use an Old Testament analogy, we, as saved people, are like levitical priests, with the priviledge of worshipping God as priests, but Jesus is a priest of the order of Melchizedek. As the Hebrew writer describes it, Jesus is a priest by virtue of his own righteousness. We certainly are not!
If we are all priests and if we have Jesus as a high priest, then Christianity does not need anything even remotely like the priesthood of Orthodox or Roman Christianity. These priesthoods are an abomination, as they usurp the relationship we have directly with the Father through Jesus. Historically, the Orthodox priesthood developed from the Christian office of the elder/overseer/shepherd. One of the Greek words for the elder is presbuteros, which morphed over time into the word priest. What was an overseer of the church (which is what a presbyter is) became a priest, with priestly clothes. By the fourth of fifth century, these “priests” were even beginning to offer the Lord’s Supper as if it were a reenacted sacrifice–something that the New Testament never anticipated.
About Isaiah 66:21, I agree that this is a prophecy about the future church/Kingdom of God. Yes, it is saying what I am saying (and what the New Testament says) which is that in future times (in other words, for us, now) there will be a new kind of levitical priesthood. We are all priests. We all have full access to God (Hebrews 10:19), and do not need earthly priests such as is found in Orthodox Christianity.