Although Romans 1:24-27 is not the only passage in the Scriptures which clearly condemns homosexual practice, it is the most demonstrative. Paul wastes few words in showing his position on the subject. (And since he is an apostle of Christ, it also would be the position of God).
27and in the same way also the men abandoned the natural function of the woman and burned in their desire toward one another, (G)men with men committing indecent acts and receiving in their own persons the due penalty of their error.
Contextually, Paul is detailing why God’s wrath has been revealed against mankind. First, he will establish the sin of the Gentiles. Then, he will establish the sin of the Jews. The conclusion will be all have sinned, and therefore face God’s wrath.
Our verses here deal with the sin of the Gentiles. The Gentiles had suppressed knowledge of the true God and instead made idols. Turning to idolatry affects not only who you worship, but how you act. Therefore, Paul lays out the sins the pagans committed.
It seems more than coincidental that both the first sin, and the one that is given the most attention, is homosexuality. I say it is not coincidental, because in order to practice homosexuality you have to deny the Creation (or at least the implications of creation). Creation teaches us that God made male and female and that marriage (which is the only place sex is to be found) is between a man and a woman (read more about that here). So, in order to practice homosexuality, you have to overlook the teaching of Creation.
In the English text Paul describes homosexuality as impurity, dishonor, degrading, unnatural, indecent, error, and deserving of a penalty. In our politically correct world, Paul would most likely be seen as a bigoted, unloving, homophobe. However, the apostle desired to show in the clearest way the sin of homosexuality as being a primary example of what happens when a society rejects God’s standards.
A first century reader studying this passage would leave with only one conclusion: Homosexuality is a sin deserving of God’s wrath.