Unless readers go on to read the rest of what Paul wrote about righteousness (and its lack), they will never grasp who “the unrighteous” are in those verses. The matter of righteousness is mentioned 7 times in chapter 3 alone! I suggest that anyone wanting to understand his initial references to who the unrighteous are in chapter 1, needs to read without stopping to the end of chapter 3, at the least. This is confirmed in “The Treasury of Scripture Knowledge”, on its notes about the book of Romans:
“The whole Epistle is to be taken in connection, or considered as one
continued discourse; and the sense of every part must be taken from
the drift of the whole. Every sentence, or verse, is not to be
regarded as a distinct mathematical proposition, or theorem, or as a
sentence in the book of Proverbs, whose sense is absolute, and
independent of what goes before, or comes after: but we must remember,
that every sentence, especially in the argumentative part, bears
relation to, and is dependent upon, the whole discourse, and cannot be
rightly understood unless we understand the scope and drift of the
whole; and therefore the whole Epistle, or at least the eleven first
chapters of it, ought to be read over at once, without stopping.” (p.
116, Bagster)
My answer, therefore, deals with what those first 3 chapters prove, for Paul there quotes Psalm 14:1-3 & 53 to bring home the full impact of what he started to say at the beginning of his letter. He starts by declaring that every person who denies the reality and claims of God is without excuse on two counts:
(1) The power of God unto salvation has been revealed through the gospel of Christ, to all who believe it; God’s righteousness has been shown in and through Christ for, via the cross and the resurrection, God dealt righteously with sin by pouring his wrath against sin upon his sinless Son, which enabled justice to be dispensed whilst simultaneously enabling his undeserved love and forgiveness to be received by sinners who put faith in that provision.
(2) That which may be known of God’s qualities and creatorship is seen in his creation, thus those who deny that evidence are without excuse.
But those who do not like to retain God in their knowledge have been given over by him to do what their unrepentant, unbelieving hearts desire to do (vss.28-31). There’s little need to single out homosexuality, for those verses also list acts of unrighteousness like fornication, wickedness, covetousness, maliciousness, envy, murder, argumentativeness, deceit, and suchlike things. It is not that all unrighteous people are homosexuals. There are plenty people in the world who would never do that but they are full of covetousness and maliciousness, or they are utterly deceitful, or they are murderers. The point of chapter 1 is to start unpacking how “the gospel of Christ is the power of God unto salvation to every one that believeth; to the Jew first, and also to the Greek. For therein is the righteousness of God revealed from faith to faith: as it is written, The just shall live by faith.’ (A quote from Habakkuk 2:4.)
Chapter 2 starts with, “Therefore thou art inexcusable, O man, whosoever thou art that judgest…” So you have to have taken on board all of chapter 1 to follow the continuation of the argument in chapter 2. Those who seek God’s righteousness are contrasted with contentious people who do not obey God’s truth, but who obey unrighteousness. “For there is no respect of persons with God, for as many as have sinned without law shall also perish without law: and as many as have sinned in the law shall be judged by the law” (vss. 8-12).
Chapter 3 then asks what advantage there is in being a Jew, and the point is made that both Jew and Gentile alike are condemned in their sin, and God is not unrighteous to take vengeance and to judge the world. This is where the Psalms are quoted, bringing us back to the point of chapter 1:
“As it is written, There is none righteous, no, not one: There is none
that understandeth, there is none that seeketh after God. They are all
gone out of the way, they are together become unprofitable; there is
none that doeth good, no, not one. Their throat is an open sepulchre;
with their tongues they have used deceit; the poison of asps is under
their lips: whose mouth is full of cursing and bitterness: their feet
are swift to shed blood; destruction and misery are in their ways, and
the way of peace they have not known; there is no fear of God before
their eyes” (Psalm 14:1-3 & 53).
And, by vs. 20 he can say,
“Therefore by the deeds of the law there shall no flesh be justified
in his sight: for by the law is the knowledge of sin. But now the
righteousness of God by faith of Jesus Christ unto all and upon all
them that believe – for there is no difference, for all have sinned
and come short of the glory of God; being justified freely by his
grace through the redemption that is in Christ Jesus …Therefore we
conclude that a man is justified by faith without the deeds of the
law.”
By now, the answer to your question should have become clear. There is no-one righteous, no, not even one. Logically, this means that all are unrighteous, from God's sinless perspective. But those who accept the righteousness of God in what he did to deal with all our sin at the cross, will be justified by God, due to faith of Jesus Christ to all who believe.
