OT, yes.
The NT points out that those practicing such things will not inherit the kingdom, along with those practicing a host of other sins. It does not recommend the death penalty for doing so. Those are two very different things.
In fact, I don't think the NT ever tries to prescribe the death penalty, imposed by a secular government, for any sin. Not that I can remember, anyway. The NT was written by men who were an itsy-bitsy and often persecuted minority in the empire. They, for fairly obvious reasons, don't seem to have thought it their duty to recommend laws to the rulers.
I pretty much agree with your description of the NT and OT views on civil govt.
John 18:36 comes to mind rather quicly too.
Jesus answered, “My kingdom is not of this world. If My kingdom were of this world, then My servants would be fighting so that I would not be handed over to the Jews; but as it is, My kingdom is not of this realm. (NASB)
“The NT... does not recommend the death penalty for doing so.”
What I said was that both the Old and New Testaments of the Bible say that those who engage in homosexual sex acts deserve death. You are free to argue that ALL sin has death as the ultimate outcome, but my point still stands that homosexual sex is specifically mentioned in both sections of the Bible as deserving the death penalty.
Grace becomes meaningless when the concepts of right, wrong and the righteous judgment of God are thrown out the window. There are those who think that the moral standards of the Law of Moses were revoked in the New Testament. That is not what it means by describing believers as not being under the Law but under grace. In fact, Jesus taught that our righteousness must exceed the righteousness of the religious law teachers of that generation. Those who are not transformed by grace ARE still condemned by the Law. (See Romans 3:19.)
Notice that the Law of Moses, in some cases, addressed the moral conduct of those who were not obligated to follow the ceremonial aspects of the Law. God said He was driving out the inhabitants of Canaan because of their wickedness, and He named some specific practices for which this judgment happened. Among them is homosexual sex. (See Leviticus 18:22-29.)
Jesus affirmed the judgment against Sodom. He said He did not come to destroy the Law but to fulfill it. He specifically mentioned the lack of repentance of Sodom that led to its destruction and also future judgment. (See Matthew 11:20-24.) Jesus also specifically named fornication as a sin, which includes homosexual sex. (I will also mention here that Jesus taught that there were sins far worse than the sin of Sodom, but this is not a justification for this sin being small, insignificant, or unimportant. It is called an abomination for a reason.)
The apostles also taught that it is a serious offence and deserves death as a consequence. It is also clear that God granted human government that authority to take a life when the death penalty is warranted. (See Romans 13:4.)
Romans 1:26-32 (partial)
For this reason God gave them up to vile passions. For even their women exchanged the natural use for what is against nature. Likewise also the men, leaving the natural use of the woman, burned in their lust for one another, men with men committing what is shameful, and receiving in themselves the penalty of their error which was due... who, knowing the righteous judgment of God, that those who practice such things are deserving of death, not only do the same but also approve of those who practice them.
As you and others have pointed out, there are many other sins which modern Christians trivialize, which also are listed among the serious offenses. This, however, does not negate the fact that homosexual sex is specifically included in the lists of sins which deserve death.
Fortunately for all of us, God does offer mercy. It is extremely important though to understand that God does not accept or wink at this behavior. He has made it exceedingly clear that it is an abomination, those who engage in it are a threat to civilization and are enemies of God, and those who do not come to agreement with God about the severity of their sin problem and cry out to Him for mercy will not only have physical death as a consequence of sin but also eternal judgment in the lake of fire.
I am not advocating a futile attempt to transform homosexuals to Christians by passing laws restraining or punishing this behavior. If laws could do this, then the Law of Moses would be sufficient. What I am saying is that Christians need to be aware of the severity of this (and all) sin, and take a stand for what is right. We must preach against sin because it is an understanding of sin that allows people to understand the Gospel and our need of salvation.
We cannot mix Law and Grace. Those who are proud and stubborn, refusing to acknowledge their sin, must understand they are under the condemnation of God’s righteous Laws. Only when a person understands this are they properly able to understand the Gospel and God’s grace.
We do not have to quote the Bible to homosexuals or homosexual advocates though. It is possible to argue from a purely secular perspective that homosexual behavior is self-destructive, harms the family and loved ones of those who engage in it, and harms society in general. Consequently, it is important to prevent or correct this behavior.