Let's say I suddenly "see the light," as it were, rush out to the nearest church to get myself baptized, and... get hit by a car and die on my way there. Is my soul still safe? In other words, is the physical act of baptism absolutely necessary for salvation with literally no exceptions, or is "baptism by desire" a real thing?
I know of no mainstream Christian church who'd say baptism is "absolutely necessary for salvation with literally no exceptions" such a view would be outside the pale of normative, historic Christian thought.
The idea of "baptism of desire" is, as far as I know, a specifically Roman Catholic approach. We Lutherans would look at it differently.
From the Lutheran POV we speak of "Word and Sacrament" as the Means of Grace. We understand that Word and Sacrament aren't referring to two things, but one thing: Word and Sacrament. Because in Lutheran theology it is the efficacy of God's Word that affects salvation by granting faith to the hearts of sinners and freely justifying them. A quote our Lutheran Confessions use comes from St. Augustine to help explain what we mean when we say "Sacrament":
"Accedat verbum ad elementum et fit sacramentum", that is to say, the joining of the Word with the element makes it a Sacrament. Sacraments are therefore "Visible Word".
Concerning Baptism the Large Catechism reads: "
From this now learn a proper understanding of the subject, and how to answer the question what Baptism is, namely thus, that it is not mere ordinary water, but water comprehended in God's Word and command, and sanctified thereby, so that it is nothing else than a divine water; not that the water in itself is nobler than other water, but that God's Word and command are added."
What is efficacious in Baptism, indeed, what makes Baptism more than just ordinary water, is God's Word. It is the Word of God, the Gospel, that is efficacious to salvation as St. Paul writes in Romans 1, "I am not ashamed of the Gospel for it is the power of God to save all who believe," and in Romans 10 speaking of this Word as what delivers faith to man from outside of himself, "For faith comes by hearing and hearing by the Word of Christ."
So, as an example, we have the thief who hangs beside Christ at the crucifixion who pleads with Jesus, "Remember me when you come into your kingdom" to which Jesus responds, "Truly I say to you, today you will be with Me in Paradise." What delivers salvation to the thief is this promise, this word which Christ speaks. This thief has assurance of salvation because He has the true and certain Word of Christ, the Son of God. This is the same Word that is joined together with water in Baptism which makes Baptism what it is. Such that St. Paul will write, "All of us who have been baptized into Christ have been baptized into His death" and "All of you who have been baptized into Christ have put on Christ"; and such that St. Peter writes, "this water corresponds to baptism which now saves you, not the removal of dirt from the flesh but as a pledge of new conscience before God in the power of Christ's resurrection".
So what does this mean? It means that if you believe--have faith--then this faith has been given to you by God, and it means you are truly and really saved; you ought then be baptized for all the reasons Scripture offers as to what Baptism means and is. If you are struck dead before being baptized your salvation is not wrecked due to the inability to receive Baptism; for if you had faith such that you desired to be baptized then your faith surely has saved you because through faith you are justified freely and found in Christ. It's not your desire to be baptized, it's the Word of God--the Gospel--which having granted you faith that is God's gracious means of delivering to you salvation, on Christ's account.
Baptism is, indeed, the means by which God brings people into Christ and thus saves them--for salvation is found exclusively in Jesus Christ, His death and resurrection--Baptism does that by the Word of God. Which is why rejecting or putting off baptism is a bad thing; that said, Baptism is not "absolutely necessary" for reasons noted already. Baptism is necessary, but not absolutely necessary; we would never suggest that there are circumstances in which God is unable to save, but trust entirely on the goodness and mercy of God to save the whole world for Christ's sake.
-CryptoLutheran