1. Treating references to homosexuality in the Old Testament as either irrelevant or directly applicable to the current question.
You see this in public debates of the issue, where extremists on both sides talk over (and past) each other. One thing they often share in common is interest in quoting passages from the Old Testament on the question. Then the person on the left reminds us that the sanction mentioned is stoning. “Do you want to stone gays?”, one shouts. “No, but I believe what the Bible says about homosexuality.” “Well, right next to that verse it says that you should stone disobedient children—Oh, and not eat pork, and not touch a woman who is having her period.” Bottom line: the skills of biblical interpretation are about equally as bad on both sides of the table.
If there’s every reason to distinguish these two covenants, we have to be very careful nonetheless that we don’t make the opposite interpretive blunder of contrasting the Old and New Testaments on the question of homosexual practice itself. I’ve heard of late several times committed Christians acknowledging that the Old Testament forbids it, but the New Testament is silent. It’s “mean Moses” versus “nice Jesus”: a familiar but completely baseless contrast. Affirming that the the civil laws are now obsolete doesn’t mean that the rationale explicitly given for some of these laws should be disregarded, especially when God singles some acts out not simply as dependent on God’s will for that time and place, but as “abominations.” Homosexuality is included in that list, as it is also in the New Testament (1 Cor 6:9; 1 Tim 1:10—right up there with “murders, enslavers, liars, and perjurers”). The church does not have the power of the sword in the new covenant. Nevertheless, God’s statement on the matter is pretty clear: he hates homosexuality. It violates the natural order—reflecting the extent to which fallen humanity will go to suppress the truth—even that which can be known by reason—in unrighteousness (Rom 1:18-32).
It should be added that Paul’s point in Romans 1-3 is to sweep the whole world—Jew and Gentile—into a heap, condemned under the law, in order to announce that Christ is the Savior of all, Jew and Gentile, and justifies the ungodly who trust in him. We are all called to repent—lifelong repentance, in fact. In this, as in everything, we fall short; our imperfect repentance would be enough to condemn us if we weren’t clothed in Christ’s righteousness. However, to repent is to acknowledge that God is right and we are wrong—on the specifics of precisely where we want to assert our sovereignty.