There's been a lot of banter back and forth at various times in this thread about Romans 1 and what it's teaching. One gent (can't recall who exactly) recently tried to diminish the universal force of vv. 18-32 by claiming that only "some" rejected God's truth that he has revealed through his physical creation. But this doesn't square at all with context of the first three chapters, which is what I'm going to set out to prove by quoting or citing a few passages mostly from within these three chapters. So...without further adieu...
Rom 3:9
9 What shall we conclude then? Are we any better? Not at all! We have already made the charge that Jews and Gentiles alike are all under sin.
NIV
"Conclude" from what? Obviously from what he wrote in the first two chapters! And what did he argue in those two chapters? He argued man's depravity from God's three-prong revelation to mankind: From Natural Revelation to all men which pertains to the external world around us that touches all our senses; then from Special Revelation (or more specifically the divinely inspired written code of the Law) as this was revealed to the Jews; then finally from Intuitive Revelation by which God internally revealed his righteous Law by writing the works of that Law on the hearts of all men, especially the Gentiles who basically were not privy to Special Revelation the way OT Israel was. In these we have God's comprehensive three-in-one Revelation of Himself in terms of His attributes, his holy Law and his holy character. This is how Paul could write that all men are without spiritual/moral excuse (Rom 1:20; 2:1). Plus all men are under sin, that is to say, all are under the penalty, power and presence of sin in this world. So, just from these passages alone, we can readily and easily see that Romans 1 applies to a lot more than just a few men or some men.
But there's even more compelling evidence of this fact from Romans 1itself; for Paul tells us in this chapter what mankind did as a result of their depravity, as this was expressed by mankind's wanton and willful rejection of God's Natural Revelation. Note this text carefully, please:
Rom 1:21-23
21 For although they knew God, they neither glorified him as God nor gave thanks to him, but their thinking became futile and their foolish hearts were darkened. 22 Although they claimed to be wise, they became fools 23 and exchanged the glory of the immortal God for images made to look like mortal man and birds and animals and reptiles.
NIV
Verse 23 tells us what depraved men did once they turned away from God and rejected him: They ALL became pagan idol worshipers! And the world has more than "some" or 'few" of such worshipers, most especially when we consider that Paul broadened the definition of "idolatry" to include the idols men erect within their own hearts due to sin (Col 3:5). Something has to fill the spiritual vacuum man has created when he rejects his Creator. And we can clearly see this truth throughout the OT and NT! Even Israel and Judah became vile idol worshipers! The need to fill this vacuum is inevitable! The sons of men MUST turn to the will of Self to create a god in their own image to their own liking. Men live to either do God's will or to do the will of Self.
Moreover, even in Paul's day, the entire known Greco-Roman world was filled with pagan idol worshipers, as we see when Paul visited Athens (Acts 17) and from the grief he suffered in Ephesus from the troublemaker Demetrius, a silversmith who fashioned idols for the population (Acts 19), etc. Even Roman emperors were worshiped as gods, just as Egyptian pharaohs before them were in the days of Moses, along with their pantheon of other gods. Therefore, idol worship was and still is to this day a universal phenomenon! Man either worships the one true God or a god of his own making!
And the last piece of evidence that Romans 1 applies universally is found in Paul's divinely inspired indictment of all mankind (Rom 3:9-18.) This indictment didn't fall on just "some" men but on all mankind because all have sinned and fall short of the glory of God (Rom 3:23).
Before ending this, I have a couple of miscellaneous observations. All men sin and fall short of the glory of God because of their inability to understand spiritual truth. This fact is pointed out twice in Rom 1-3 (1:31; 3:11), all of which harmonizes nicely with 1Cor 2.
Rom 1:21 teaches that the sons of men became vain (or futile) in their thinking, and as a result they became idol creators and worshipers. This shouldn't surprise any of us since those who live in the flesh (which all unregenerates do!) have minds that are hostile towards God, not able to subject itself to the law of God, and for these reasons such men cannot please God (Rom 8:7).