Most Protestants today recognize only one mediator between them and God, Jesus Christ (1 Tim 2:5). The doctrine of the “priesthood of all believers” was revisited and restored at the time of the Reformation. The veil has been torn and, through Christ, we have been given direct access to God, just like a priest of old. But, the “Priesthood of all believers” idea is not NEW to the New Covenant. R.J. Rushdoony said this: “It is a Protestant fallacy that ‘the priesthood of all believers’ is a ‘New Testament doctrine’ which came to light with the Reformation.”
Ex 19:5-8 says this, “Now therefore, if you will indeed obey my voice and keep my covenant, you shall be my treasured possession among all peoples, for all the earth is mine; and you shall be to me a kingdom of priests and a holy nation. These are the words that you shall speak to the people of Israel.” So Moses came and called the elders of the people and set before them all these words that the Lord had commanded him. All the people answered together and said, “All that the Lord has spoken we will do.” And Moses reported the words of the people to the Lord.”
So God desired Israel to be to Him a kingdom of priest’s right from the beginning and they agreed. But notice what happened right after Moses brought the Ten Commandments to Israel and God displayed His great power. Right after He gives them the Ten Commandments we read, “Now when all the people saw the thunder and the flashes of lightning and the sound of the trumpet and the mountain smoking, the people were afraid and trembled, and they stood far off and said to Moses, “You speak to us, and we will listen; but do not let God speak to us, lest we die.” (Ex 20:18-19) Instead being honored to be a "kingdom of priests" the Israelites were afraid of God and asked Moses to be their mediator.
Jay Rogers explains the result of Israel's decision to have a mediator between them and God, “God honored the people's desire to have a mediator by choosing Moses, Aaron, Nadab and Abihu, and the seventy elders of Israel to minister to God in a complicated ritual of daily sacrifices. The Levitical Priesthood was established to do the work of the ministry and only Moses was allowed to come directly into God's Presence. The people were not even allowed to draw near to God and the elders could only worship at a distance. The God of Israel hoped that the drudgery of service in a ritualistic system of religion would cause the people to yearn for something more.”
Many people know the story about Israel wanting and choosing a king to rule over them to be like all the other nations. Most don’t realize they also chose a mediator to intercede for them. So Israel not only chose a king to rule over them they also chose a priest to mediate for them. But it’s always been God’s perfect will for God’s people to be a nation of kings and priests. Thank God He sent His son to make it possible for us, as it was meant to be, to again have direct access to the throne-room of God. “But you are a chosen race, a royal priesthood, a holy nation, a people for his own possession, that you may proclaim the excellencies of him who called you out of darkness into his marvelous light.” (1 Peter 2:9)