A particular form of intercourse (one which is practiced by both heterosexuals and homosexuals) may well have been involved in the case of Sodom and Gommorah, but it was not the only or, at least according to Ezekiel, primary reason for its destruction.
Ezekiel 16:49-50
49 " 'Now this was the sin of your sister Sodom: She and her daughters were arrogant, overfed and unconcerned; they did not help the poor and needy. 50 They were haughty and did detestable things before me. Therefore I did away with them as you have seen.
socialaction.com/education_resources/weekly_torah/bereshit_genesis/Vayera/SinofSodom.shtml
The Torah did not elaborate on the sin of Sodom, but the underpinnings are expressed later in the prophecy of Ezekiel: “Behold this was the sin of Sodom…She and her daughters had pride, excess bread, and peaceful serenity, but she did not strengthen the hand of the poor and the needy” (16:49). The prophet’s description combined with what the Torah reveals to us gives us the following picture: the people of Sodom insisted on preserving their high quality of living to such an extent they established a principle not to let the poor and homeless reside in their city. Consequently when a destitute person would come seeking help, they would revoke his right to any welfare—public or private! By doing this they figured they would preserve an elite upper class community who would monopolize the profits that the bountiful land offers without having to distribute any revenues to a “lower class” of people.
An opinion in the Mishna in Avot 5:10 further strengthens this picture of moral depravity when it defines the Sodomite as one who says, “What’s mine is mine and what’s yours is yours.” The Mishna decries a man who wishes to remove himself from the social responsibility of welfare by closing himself and his wealth from others, even if he makes the claim that he is not taking away from anyone else.
Given that, however, you are still left with the fact that American civil law is not determined by the laws of any particular religion, Christian, Jewish or otherwise. What is being discussed is civil marriage, not religious sacramental marriage. The one does not require that the other be granted.
