As I'm reading this I was thinking about how being a priest at this time in history would not have been a big occupational desire for me. The pressure to follow all the instructions God gave perfectly or risking death seems a bit extreme for me. I'm thinking that there would have been a small group of people willing to take on such a role. And after the deaths of Nadab and Abihu I would think that all the other priests were a bit nervous as they completed their tasks.
A couple things stand out to me from the passages about the death of these two priests.
First, we are told that they sinned by "offering strange fire before the LORD". We are not told precisely what kind of sin this was but it clearly shows that this was an act of direct disobedience to God. I think likely we are not told of the specific sin so that our focus is not removed from the underlying sin of disobedience.
Also, they must have agreed among themselves that this was what they should do, as they were both put to death for it. Just because we can find others who agree with us does not make us right.
When I read the accounts here in Leviticus of the perfection expected by these imperfect humans I think that the people of that time must have felt that there had to be a better way (at least that's what I would have been thinking). I appreciated this comment in this article Principles of Priesthood.
Israel would be painfully aware of the limitations of this Aaronic Priesthood. Thus they would be prepared for and looking forward to a “better Priest and priesthood” which would be the result of the New Covenant and of the coming of the Christ. The Aaronic priesthood was shown to have failed at its very outset. It is as though an unsinkable ship was launched, and at the first instant it struck the water it sank. If these two priests, Nadab and Abihu were so sinful as to be struck dead by God, how could anything they or any other sinful priest did bring people to perfection? Any system which had an imperfect priesthood could surely not bring the people to perfection. The flaws of the old covenant and its Aaronic priesthood pointed to the need for a new and better covenant, with a better priesthood. The Aaronic priesthood was only a provisional, imperfect priesthood. A sinner was the high priest, and his sinful sons were priests as well. There was no basis for unbridled optimism in the Aaronic order.
I'm so glad that this Levitical Priesthood came to an end with Jesus and that a new priestly order of all of those who accept Him as their Savior can be united with Him through faith.
Since therefore, brethren, we have confidence to enter the holy place by the blood of Jesus, by a new and living way which He inaugurated for us through the veil, that is, His flesh, and since we have a great priest over the house of God, let us draw near with a sincere heart in full assurance of faith, having our hearts sprinkled clean from an evil conscience and our bodies washed with pure water. Let us hold fast the confession of our hope without wavering, for He who promised is faithful; and let us consider how to stimulate one another to love and good deeds, not forsaking our own assembling together, as is the habit of some, but encouraging one another; and all the more, as you see the day drawing near (Heb. 10:19-25, emphasis mine).
“But do not be called Rabbi; for One is your Teacher, and you are all brothers. And do not call anyone on earth your father; for One is your Father, He who is in heaven. And do not be called leaders; for One is your Leader, that is, Christ. But the greatest among you shall be your servant. And whoever exalts himself shall be humbled; and whoever humbles himself shall be exalted” (Matt. 23:8-12).
You also, as living stones, are being built up as a spiritual house for a holy priesthood, to offer up spiritual sacrifices acceptable to God through Jesus Christ. … But you are a chosen race, a royal priesthood, a holy nation, a people for God’s own possession, that you may proclaim the excellencies of Him who has called you out of darkness into His marvelous light (1 Pet. 2:5, 9).
And He has made us to be a kingdom, priests to His God and Father; to Him be the glory and the dominion forever and ever. Amen (Rev. 1:6).