While God holds each individual accountable for their response to the propensity to sin, according to the law written upon their hearts(the imprint of the divine nature- the Lamb slain), and the alternative to chose righteousness...
Ro 1:18 For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who suppress the truth in unrighteousness, 19 because what may be known of God is manifest in them, for God has shown it to them. 20 For since the creation of the world His invisible attributes are clearly seen, being understood by the things that are made, even His eternal power and Godhead, so that they are without excuse
Ro 2:6 But in accordance with your hardness and your impenitent heart you are treasuring up for yourself wrath in the day of wrath and revelation of the righteous judgment of God, 6 who “will render to each one according to his deeds”: 7 eternal life to those who by patient continuance in doing good seek for glory, honor, and immortality; 8 but to those who are self-seeking and do not obey the truth, but obey unrighteousness—indignation and wrath, 9 tribulation and anguish, on every soul of man who does evil, of the Jew first and also of the Greek; 10 but glory, honor, and peace to everyone who works what is good, to the Jew first and also to the Greek. 11 For there is no partiality with God.
12 For as many as have sinned without law will also perish without law, and as many as have sinned in the law will be judged by the law 13 (for not the hearers of the law are just in the sight of God, but the doers of the law will be justified; 14 for when Gentiles, who do not have the law, by nature do the things in the law, these, although not having the law, are a law to themselves, 15 who show the work of the law written in their hearts, their conscience also bearing witness, and between themselves their thoughts accusing or else excusing them) 16 in the day when God will judge the secrets of men by Jesus Christ, according to my gospel.
....(imo) the propensity for sin is genetically locked in through Adam, and each and every one has at sometime made that archetypal choice, affirming their heritage in the first man, engendering death, except for Jesus the Messiah, who made a righteous choice(a faithful sacrifice rather than sin).
Acts 3 Therefore having overlooked the times of ignorance, God is now declaring to men that all people everywhere should repent, 31 because He has fixed a day in which He will judge the world in righteousness through a Man whom He has appointed, having furnished proof to all men by raising Him from the dead.”
So in the first man, Adam, all have chosen sin, affirming their heritage, and are individually accountable for it, and in the second man Christ, all have chosen righteousness(repentence, contrition, forgiveness, faith) and are individually justified by Him, becoming part of the corporate new man, His heritage(many sons unto glory).
So original sin is(imo) not necessarily false doctrine, as with so many doctrines- depending on the individual understanding and scope of application.
The only deed that will satisfy the righteousness of God is a broken and a contrite heart(repentence and faith before the Lordship of Jesus)- the rest springs forth from there.