Main point summary
God's righteousness has been shown intact and apart from the law because God has graciously gifted justification through Christ's blood.
But now a the righteousness of God b has been manifested apart from the law,
although c the Law and the Prophets bear witness to it—
the righteousness of God d through faith in Jesus Christ for all who believe.
e For there is no distinction:
for f all have sinned
and fall short of the glory of God,
g and are justified h by his grace as a gift,
i through the redemption that is in Christ Jesus,
whom God j put forward as k a propitiation l by his blood,
to be received by faith.
This was to show God’s righteousness,
because in m his divine forbearance he had passed over n former sins.
It was to show his righteousness at the present time,
so that he might be just
and the justifier of the one who has faith in Jesus.
The ESV translation here is misleading - it looks like it should be a concessive, but is actually a participle in the Greek and therefore behaves more like a comparison (although a true relationship is hard to nail down).
This lack of distinction is regarding Jews and Gentiles, which is being discussed in this chapter; whereas it would seem that Jews have an advantage over Gentiles for having the law, in fact there is no difference - all are under the curse of sin.
God's righteousness was in doubt, because sin requires death yet had been overlooked until this point. He had passed over former sins in anticipation of the final solution; Jesus' death re-establishes God's righteousness, that is, His justice and His justifying grace.
"the glory of God" could be God's glorious standard, or could be God's literal glory; it would seem to be God's glorious standard, but there might be some interplay between the law and the literal glory of God.
Grace is often understood as a gift - why add "as a gift" after grace?
Not that He became just, as thought He somehow wasn't just before, but that He is shown indeed to be just.
Lest we think we have any hand in this; God put Jesus forward, that is, offered Jesus as a propitiation to Himself. We caused the problem, God had certain requirements to deal with the problem, God Himself gave the solution to His requirements.
Works are meaningless when it comes to propitiation. We are propitiated by faith alone; nothing can "propitiate more", as it were - the final propitiation is in Jesus, and is received (not earned or attained or gained) by faith .
God's righteousness is of utmost concern to Paul here - our salvation and justification is only brought in to maintain God's righteousness. We do well to keep this straight: God's primary concern is Himself, and is only secondarily concerned with us. This does not diminish His love for us, since He did indeed redeem us through the blood of Jesus; but it does mean we need never to make a god of ourselves, either to ourselves or to God - we are loved, but we are not the center of God's attention, and therefore we should not make ourselves the center of our own attention either.