It is not that a passage such as Romans 1 is unclear. It is clearly no endorsement of Homosexuality.
Rom 1:26 For this reason God gave them up to dishonorable passions. For their women exchanged natural relations for those that are contrary to nature;
Rom 1:27 and the men likewise gave up natural relations with women and were consumed with passion for one another, men committing shameless acts with men and receiving in themselves the due penalty for their error.
Moreover, it is in the NT, and makes no reference to OT commands, so there is no question of whether it is now obsolete under the new covenant, which many in the other thread seemed to jump on regarding other texts.
And unlike some other texts it does not depend on the definition of a single word. You referenced the text in I Corinthians in the other thread. Some debate the meaning of the word used in that text. However, in Romans 1 this is not the case. The passage is not reliant on only one word to convey what he is talking about.
Moreover, you cannot claim, as some do in looking at some controversial passages, that Paul was simply addressing a local situation, rather than universal principles. The context does not really allow for that here. The passage is actually part of a long section where Paul is essentially presenting a case for all of humanity being sinners, and in need of salvation. And it chronicles the slouching of humanity in general further into sin, not a particular local situation.
The argument begins in 1:18 with a blanket argument to show that no one could claim they were ignorant of God:
Rom 1:18 For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who by their unrighteousness suppress the truth.
Rom 1:19 For what can be known about God is plain to them, because God has shown it to them.
Rom 1:20 For his invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made. So they are without excuse.
Then it goes on to show that though men knew God, they did not worship Him and were darkened, falling further and further into sin.
Romans 1 is likely intentionally provocative towards Jewish readers, as it points out what they would consider to be some of the more revolting sins practiced among the Gentiles, such as idolatry and homosexuality. But then he turns the tables in chapter 2 showing how those who condemn folks who do these sins are likewise under sin, and in need of the grace revealed in Christ.
Rom 2:21 you then who teach others, do you not teach yourself? While you preach against stealing, do you steal?
Rom 2:22 You who say that one must not commit adultery, do you commit adultery? You who abhor idols, do you rob temples?
Rom 2:23 You who boast in the law dishonor God by breaking the law.
Rom 2:24 For, as it is written, "The name of God is blasphemed among the Gentiles because of you."
Rom 2:25 For circumcision indeed is of value if you obey the law, but if you break the law, your circumcision becomes uncircumcision.
The entire argument builds to chapter 3 where it is shown all have sinned and are in need of grace:
Rom 3:19 Now we know that whatever the law says it speaks to those who are under the law, so that every mouth may be stopped, and the whole world may be held accountable to God.
Rom 3:20 For by works of the law no human being will be justified in his sight, since through the law comes knowledge of sin.
Rom 3:21 But now the righteousness of God has been manifested apart from the law, although the Law and the Prophets bear witness to it—
Rom 3:22 the righteousness of God through faith in Jesus Christ for all who believe. For there is no distinction:
Rom 3:23 for all have sinned and fall short of the glory of God,
Rom 3:24 and are justified by his grace as a gift, through the redemption that is in Christ Jesus,
Rom 3:25 whom God put forward as a propitiation by his blood, to be received by faith. This was to show God's righteousness, because in his divine forbearance he had passed over former sins.
So the context is universal here, not a local situation. It is talking generally about the sin problem. So I would say Romans 1 is particularly helpful in this discussion. It is not dependent on OT commands, is not dependent on the definition of one word in describing the sin in question, and it is found in a universal context.
While you did get mostly responses from atheists in the other thread, I would just say that one poster did seem to touch on the heart of the issue. The issue is differing approaches to Scripture in general.
The issue is not that a text such as Romans 1 is unclear on the subject. The problem is some folks do not view the Scriptures as the be-all-end-all of revealing God's nature or will.
Some view each word of Scripture as inspired, and representing the views of God. Others see that some elements may be inspired and universal, and other things may be more representative of the views of the human instrument, or perhaps at best a dim reflection of God's views, but not the whole story.
Essentially, those who take the view that the church should embrace homosexuals who are still practicing homosexual sex are not basing this claim on any of the specific texts regarding homosexuality. Instead they are trying to say that those texts represented Paul's views, or the view of the culture, and that the love for all portrayed in other parts of Scripture show God's true intent.
To me they must explain away quite a bit to get to that point, and I cannot join them in that interpretation. But they can defend their stance if the like.
To me Paul clearly taught that Christ is the solution to the sin problem, through forgiveness of sins, but that this also results in a changed life. That does not mean excusing sin but being cleansed of it and repenting of it, and walking in the Spirit to crucify the desires of the flesh.
This by no means indicates any of us are sinless, or anything other than sinners saved by grace, and living in Him by grace.