Paul no sooner declares that the Gospel is for everyone than he jumps to the universality of God's wrath (Rom 1:18-32, Rom 2:1-16).  Before he can talk about righteousness, Paul starts with the negative reality -- which is, that men are not in right-standing with God.  This might be obvious to his Jewish readers, who have been raised with a strong morality and sin-consciousness, but it could not be assumed in Gentiles.  Paul makes the amazing assertion that all men have a basic knowledge of God, even apart from Old Testament Scriptures:

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           "For since the creation of the world God’s invisible qualities—his eternal power and divine nature—have been clearly seen, being understood from what has been made, so that men are without excuse" (Rom 1:20).

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            Despite having this knowledge of God, men did not worship Him or give thanks to Him, but

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           "their thinking became futile and their foolish hearts were darkened" (Rom 1:21).

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This wrong-thinking led to idolatry.  Instead of worshipping the Creator, men bowed before images of creatures.  Therefore, "God gave them over" (Rom 1:24) to sexual depravity, specifically homosexuality.  But beyond that, God abandoned them to "a depraved mind."  King James version calls it "reprobate."  Paul's meaning of this term is detailed in the next three verses:

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           "They have become filled with every kind of wickedness..." (Rom 1:29),

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            and his list of sinful attitudes goes far beyond the sexual realm: greed, murder, deceit, gossip, arrogance, disobedient, ruthless, and more.  Those who do such things, Paul says, deserve death.

          

In this argument, Paul seems to be mainly addressing the Gentiles.  The Jews have explicit prohibitions in the Mosaic Law (and the Ten Commandments) against both idolatry and sexual misconduct, as well as many other sins.  That was the point of the Law -- providing a standard of conduct so that one could avoid the judgment of God.  But the Gentiles had no such written standard -- therefore, how could they be judged?  Paul was saying that the reason for their culpability lay in natural revelation -- if they had properly honored the Creator, their minds would not have been confused and given over to licentiousness.