In this article, we'll be asking the exegetical question, "What relevance does Romans 1:27-8, 1 Cor. 6:9, and 1 Tim. 1:10 have to homosexuality?"
Let's start with Romans:
And likewise also the men, leaving the natural use of the woman, burned in their lust one toward another; men with men working that which is unseemly, and receiving in themselves that recompense of their error which was meet.
There's plenty of contrived exegesis available which claims that this verse is not addressed to everyday homosexual behavior but to temple prostitution, and non-homosexuals engaging in homosexual sex against their own nature.
The latter point, though perhaps an "out" for some exegetes (including Byrne, whose commentary on Romans is our primary source) begs the question of reading modern understandings into an ancient text; and whether indeed homosexuality is a natural inclination, an argument that is beside our mission statement to evaluate.
However, taken within the historical and social context, there is simply no way that one can read this as a condemnation against only "temple" acts which permits a "non-religious" homosexuality.
As Byrne points out [65-9; see also Dunn, Romans, 65-6] Paul here draws upon a "conventional polemic against the Gentile world and its idolatry." The Jews regarded homosexuality for whatever reason as a sin -- period. It was regarded as shameful because it "blurred the all-important distinction of gender role."
This leads to a conclusion that cannot be got around: Since Paul drew on this conventional polemic, there is no way that this can be an "against temple sex only" position, because according to Jewish thought, this sort of homosexual behavior was a symptom of Gentile idolatry. It is because they were idolaters that they engaged in the sinful homosexual act, which was sinful completely apart from religious considerations.
That's the simple fact of the matter, and while one could theoretically get around this with a proposition of homosexuality being inborn, practically speaking there is no getting around the clear message of Paul -- via his Jewish forebears -- that the homosexual act as a choice is manifestly a sinful one.
Now for Corinthians (and Timothy, which we need not quote for it just uses a word found in Corinthians):
Know ye not that the unrighteous shall not inherit the kingdom of God? Be not deceived: neither fornicators, nor idolaters, nor adulterers, nor effeminate, nor abusers of themselves with mankind, Nor thieves, nor covetous, nor drunkards, nor revilers, nor extortioners, shall inherit the kingdom of God?
There's also a lot of claiming that understanding "effeminate" in terms of homosexuality is misleading and that the word means "soft" or "vulnerable" and probably refers to those who are unreliable or lacking in courage.
That's certainly not supported by other uses of the same word (malakos): Witherington's Corinthians commentary  notes uses of it referring to a "young male prostitute". Lexicons like BAGD, as Wold notes in Out of Order , clearly say that the word is used of "men and boys who allow themselves to be misused homosexually" and cites "numerous examples from Greek literature" of the word used this way.
Critics argue in reply that the word has no specific referent for the homosexual act, just having feminine characteristics, but of course the "passive" partner in such a relationship DOES act out that very sort of characteristic. In addition, Wold notes  that at Paul's time, the common preference for a "passive" homosexual partner WAS one that was effeminate (whereas prior to the 5th century BC, the preference was for a masculine partner).
Finally, other Greek terms for the passive partner, clearly used in homosexual contexts, are words that have no "inherent" homosexual meaning but are borrowed words used to describe the passive homosexual. Critics have a substantial burden to carry before they can simply dismiss this word.
The reference to "abusers of self with mankind" uses a word also found in 1 Tim. 1:10 (arsenokoitai). Critics try to make some issue of this being an "obscure" or "uncertain" word for Paul's use of it seems to be the first ever use of it.
The idea that it means male-female sex is a false move; the two parts of the word mean "male" and "sexual intercourse," and Paul hardly needed to invent a word male-female sex.
Furthermore, the word is clearly derived from the LXX translations of Lev. 18:22 and 20:13, which used the words arsenos koitin and arsenos ou koimethese. Paul is merely creating a compound word from two clear words used of homosexual relations in Leviticus. It also ought to be noted that with these two words Paul would cover the "passive" and "active" role in the male homosexual relationship [Wold, 191] recognized by classical Greek writers.