Although the OT command in Israel to Israelites was that such persons broke the covenant and thereby deserved capital punishment, this doesn't apply to Christians in the New Covenant. In the New Covenant, homosexuality is still considered sinful, yet it is not an unforgivable sin.
So God changed his mind?
What a great question. In short, God didn't change his mind. The context of my paragraph was discussing the difference between the spirit and the letter of the law. Or the literal and the purpose of the law.
The law in substance remains the same. The context or circumstances determine the application. When the law was written originally it was applied in the circumstance when Israel was its own nation and was not captive to another society. You will note that when Israel was either in captivity or as a nation was taken over by another nation, the law was not applied in the same way. Mostly, this was because they didn't have the authority or jurisdiction to simply kill people or sanction people. After all, they were not the law in these new circumstances.
The law of substance is the same. And by the way, it is not even about homosexuality. It is about marriage. In God's law, marriage is a fundamental part of life and is between a male and a female. Whenever this marriage covenant was violated by adultery, polygamy, homosexuality, paedophilia, incest, and bestiality, then the marriage suffered the natural curses of that breach of covenant. A breach of that covenant under Israelite law had a maximum penalty of capital punishment. Sometimes the government was consistent and sometimes it was not. After all, governments back then like ours today, were corrupt. And this included the courts too. And sometimes the government was non-existent. The government of Israel didn't come into effect until the time of Moses. Hence, covenant breakers before then suffered in different ways for their breaches.
In the NT, Christians are in a different context and circumstance as well. We are not a nation as it were. We don't have a central government or the authority to push criminal or civil sanctions. Mostly, we are people living in the culture and the jurisdictions of nations that are opposed to the God of the Bible.
Of course, if the Christians in America rose as one and utilised the ordinary democratic system of America and wanted to bring back the death penalty for homosexuals, it would be quite consistent with the democratic principles of America. After all, whatever the majority think is right - is right and whatever the majority thinks is wrong is wrong. (I don't subscribe to that view - but those who believe in the will of the people must).
In the OT, homosexuality was not an unforgivable sin either. So the law of God has not changed. In substance, it still is an attack against marriage and family. Yet the application of how this breach of it is dependent upon the nation which has jurisdiction. Romans 13 tells Christians to obey the law of the land, except when it asks them to sin. To not put them to death is not a sin. Even in the OT, the death penalty in the appropriate jurisdiction was still only the maximum penalty.
So in length, God has not changed his mind. The law remains the same. The application of it is applied depending upon the circumstances - and one of those factors includes what the law and jurisdiction of the land is. I hope that makes sense. And if it doesn't then, I apologise. Please ask further questions and I will attempt to explain.