It says much more than that. Those people made a choice to not worship God. If God wanted to have 100% sovereignty then why does it say "since they did not see fit to acknowledge God, [then] God gave them up"? (Romans 1:28) It seems to me that Man's choice caused God to react in a certain way.
What I'm seeing is God's divine attributes and eternal nature was made known to man.
'But now', and that phrase will come up in the third chapter, God's righteousness is revealed:
For in it the righteousness of God is revealed from faith to faith; as it is written, “The just shall live by faith.” (Romans 1:17)
When it comes to being a sinner we didn't have a lot of choice in that matter, but we are all aware of certain things about God. One of the worst things God can do to you is to turn you over to your sin or as a preacher friend of mine was fond of saying, sometimes the worst thing about a sin is the sin. This is pretty clear that we all knew God, Jews knew God and so did Gentiles and for whatever reason decided to pursue things they knew were wrong. So God as an act of judgment turned them over to their sin:
Therefore God also gave them up to uncleanness, in the lusts of their hearts, to dishonor their bodies among themselves, who exchanged the truth of God for the lie, and worshiped and served the creature rather than the Creator, who is blessed forever. Amen. (Rom. 1:24,25)
Sure that's free will but so is receiving the gospel. Sin isn't just something you do, of course it is, it's something you lack and that is righteousness. There is only one source for that, the righteousness that comes by faith. God's nature has two aspects, there are attributes that are communicable and incommunicable. Of course we can't be omnipotent but we can and must bear fruit. When Jesus was describing how the gospel worked he said it's like seed, if it's not stolen away by the devil from unbelief, it's not shallow soil that withers at the first sign of trouble or isn't chocked out by the cares of this world and the deceitfulness of riches it bears fruit.
There are plenty of examples but the Corinthians are a pretty solid example, they said 'all things are lawful' (1 Cor. 6:12) but Paul says yes, 'but not all things are helpful'. Bottom line, Flee sexual immorality (1 Cor. 6:18). I know so many Christians that think somehow they are not sinners, I think they grossly underestimate sin. Paul is explaining that sin has a slavish effect which is something that God will hand you over to because he has and will.
The creation was subjected to the ravages of sin, there is no escaping that tragic truth, but there is hope:
For the creation was subjected to frustration, not by its own choice, but by the will of the one who subjected it, in hope (Rom. 8:20)
That one was a break through for me, as unpleasant as the reality of sin is it underscores the need for grace.
You're missing the point of Romans 1 through Romans 3. The point is that all peoples, (the Godless Pagans that reject general revelation in Romans 1, and the Jews that have the law in Romans 2, but don't keep it ) are guilty before God and every mouth must be stopped.
His conclusion is that all men are under condemnation and guilty before God.
But don't stop there. Keep reading further into the book, God makes it clear that among this condemned lump of clay God has the freedom to have mercy on whom He wishes.
I agree with others here that point out that man freely and willingly seeks and chooses according to his nature, which is fallen.
Agreed but Romans 3 has a turning point:
But now the righteousness of God apart from the law is revealed, being witnessed by the Law and the Prophets, even the righteousness of God, through faith in Jesus Christ, to all and on all who believe. For there is no difference; for all have sinned and fall short of the glory of God (Rom. 3:21-23)
The word used here, 'propitiation', has it's roots in the Day of Atonement when blood was sprinkled on the mercy seat. The concept of atonement was so difficult to express that William Tyndall basically invented the term 'atonement' (G2643 καταλλαγή katallagē. Romans 5:10–11; 2 Corinthians 5:18–20; Colossians 1:20, 22; Ephesians 2:16)
whom God set forth as a propitiation by His blood, through faith, to demonstrate His righteousness, because in His forbearance God had passed over the sins that were previously committed. (Rom. 3:25)
The watershed of redemption comes down to two words, 'but now'. Now free will has another choice.
Grace and peace,
Mark