I find it weird that within some Christian circles, much is made out of the fact that we are all priests and kings. The point that Paul is making here is that we are all equal. There is no hierarchy in the Christian faith except for one. And that one is our Lord, he is our King, he is our high Priest, he is the forgiver of our sins. Just as all are equal, because all have sinned and fallen short of God’s glory – likewise the free offer of forgiveness is given to all, which again makes us all equal.
For those who make a big deal out of kingship: I would remind you that the Prophet Samuel makes the point that God is displeased with the ancient Israel request for a king and actually punishes them for it with a huge storm which wipes out their wheat harvest. As for me, I am no king! I am but the adopted son of the king, in which he raises us all as equals.