Let’s address the elephant in the room: this punishment may seem a bit harsh. All that Nadab and Abihu did was perform their duty in just a slightly wrong way, and God took their lives on the spot. Is it really that important that every single commandment of God be followed to the letter? Well, the question sounds ridiculous when we actually ask it.
Yes, of course it’s that important. Our worship of God is an enormously holy matter, because God is enormously holy. But Nadab and Abihu treated it as trivial and tried to do it an easier way. They treated the worship of the Lord with carelessness, as if it were something to check off a list rather than something that demanded the devotion of their heart and soul and strength. If they treated an enormously holy matter this way, is it any wonder that the punishment was equally enormous?
I have had friends that have downplayed holy matters in a similar fashion. Many Christians do it; even some whole churches do it. No, God isn’t evaporating all those Christians with fire like he did before—hallelujah for his grace!—but it’s no less important. Besides, this was the first day of the work of the priests; if God had let that error slide, the priests would see no reason to continue handling holy matters lightly. An example needed to be set for Aaron and his other sons, as well as for us today, to show that God took these things seriously, and we should too.
The root of the matter is this: God must be glorified. As our creator, sustainer, savior, and loving redeemer, he deserves all the glory from us; and so to not give it is fundamentally untruthful. When we worship, or when we take the Lord’s Supper or get baptized or in any other way seek to glorify God, we do so as seriously, reverently, and obediently as possible, not as a passing nonchalant activity. It really is a bigger deal than we think. God is holy; our worship ought to be no less holy! To God be the glory forever and ever!