Will all believers be priests in the Kingdom?

In the Revelation Study, Pastor Armstrong mentions that the average person living in the Millennial Kingdom may never see Jesus in his Temple because only priests can go into the "Holy of Holies," but doesn't Peter call all believers priests?

All believers in the church today are called priests, as you said, because our bodies collectively are the temple of God (1Cor 6:19). Christ dwells among men on earth by His Spirit in the bodies of believers.

In the Kingdom to come on earth, however, the temple will no longer be our physical bodies. Instead, a new physical temple building will be constructed for the Kingdom period, according to Ezekiel and Isaiah, and the Lord will inhabit that building as He once did in Israel’s past.

The best description of Jesus entering the Kingdom temple is given in Ezekiel 43. The prophet was shown a vision of the future temple (which Ezekiel calls the “house” of the Lord) as the Lord enters to reign:

Ezek. 43:1 Then he led me to the gate, the gate facing toward the east;
Ezek. 43:2 and behold, the glory of the God of Israel was coming from the way of the east. And His voice was like the sound of many waters; and the earth shone with His glory.
Ezek. 43:3 And it was like the appearance of the vision which I saw, like the vision which I saw when He came to destroy the city. And the visions were like the vision which I saw by the river Chebar; and I fell on my face.
Ezek. 43:4 And the glory of the Lord came into the house by the way of the gate facing toward the east.
Ezek. 43:5 And the Spirit lifted me up and brought me into the inner court; and behold, the glory of the Lord filled the house.
Ezek. 43:6 Then I heard one speaking to me from the house, while a man was standing beside me.
Ezek. 43:7 He said to me, “Son of man, this is the place of My throne and the place of the soles of My feet, where I will dwell among the sons of Israel forever. And the house of Israel will not again defile My holy name, neither they nor their kings, by their harlotry and by the corpses of their kings when they die,
Ezek. 43:8 by setting their threshold by My threshold and their door post beside My door post, with only the wall between Me and them. And they have defiled My holy name by their abominations which they have committed. So I have consumed them in My anger.
Ezek. 43:9 “Now let them put away their harlotry and the corpses of their kings far from Me; and I will dwell among them forever.

Notice that in the Kingdom, Jesus will appear as the Shechinah glory of God, not as a man as in the days He first walked the earth. Furthermore, the Lord declares He will never leave His throne in the house of the Lord again. Therefore, in order for Jesus to be seen during the Kingdom, a person must have access to the Holy of Holies or some other part of the Millennial Temple. You may find the Ezekiel Study helpful.

Furthermore, during the time of the Kingdom, the Lord institutes a new Kingdom Law. The Kingdom law brings with it a new priesthood (see Heb 7:12). The requirements of the Kingdom law are given in Ezekiel 44-46, and in Ezekiel 40-43 we learn that Levitical priests will once again live around and officiate in the Kingdom temple.

Isaiah tells us that all the Kingdom nations will have the opportunity to witness the glory of Christ in the temple:

Is. 66:18 “For I know their works and their thoughts; the time is coming to gather all nations and tongues. And they shall come and see My glory.
Is. 66:19 “I will set a sign among them and will send survivors from them to the nations: Tarshish, Put, Lud, Meshech, Tubal and Javan, to the distant coastlands that have neither heard My fame nor seen My glory. And they will declare My glory among the nations.
Is. 66:20 “Then they shall bring all your brethren from all the nations as a grain offering to the Lord, on horses, in chariots, in litters, on mules and on camels, to My holy mountain Jerusalem,” says the Lord, “just as the sons of Israel bring their grain offering in a clean vessel to the house of the Lord.
Is. 66:21 “I will also take some of them for priests and for Levites,” says the Lord.
Is. 66:22 “For just as the new heavens and the new earth which I make will endure before Me,” declares the Lord, “So your offspring and your name will endure.
Is. 66:23 “And it shall be from new moon to new moon and from sabbath to sabbath, all mankind will come to bow down before Me,” says the Lord.

Notice Isaiah says that all nations will see Him in the temple, and the Lord will take some of the people of these nations as His priests. Therefore, priests will include Gentiles in this period. If we are selected to be a priest in the temple, then we will have access to the glory of Christ in a regular way. Otherwise, our access will be more limited as a worshipper.

Therefore, we know the nations will see Christ’s glory in some limited fashion, but what they experience will not be what the first-century disciple experienced. The world will see the glory of Christ in ways similar to how Israel saw the Shechinah glory of God in the Old Testament. Periodically and in a limited fashion.

In summary, the Church saints are priests today, because the temple of God resides in our bodies, but in the Kingdom, the temple changes as does the law, and therefore the priesthood changes as well.