What we can easily do is look at what Scripture says. In Isaiah 1:10-20 we hear a lot about evil and what one must correct, but the call is not to refrain from same-sex sexual activity but "to seek justice, rescue the oppressed, defend the orphan, plead for the widow." (vs. 17) and that fits right in with what the men of Sodom and Gomorrah are shouting about. The rape is not about the gender of the visitors but about degrading the visitors (Genesis 19:9). The lack of hospitality – the lack of protection for the weak, the poor, the outsider, and the stranger – is condemned and the specific actions of rape (symptomatic of the way strangers in the city were treated) rather than all same-sex sexual activity is what is forbidden.
There are other passages of Scripture that talk of Sodom or Sodom and Gomorrah. Without exception they focus on the crime of not welcoming the stranger rather than the sexual actions. Our modern ideas about Sodom and Gomorrah and the sins they encompassed being sexually based are plain wrong and contrary to scripture.
 Hear the word of the LORD, you rulers of Sodom! Listen to the teaching of our God, you people of Gomorrah!  What to me is the multitude of your sacrifices? says the LORD; I have had enough of burnt offerings of rams and the fat of fed beasts; I do not delight in the blood of bulls, or of lambs, or of goats.  When you come to appear before me, who asked this from your hand? Trample my courts no more;  bringing offerings is futile; incense is an abomination to me. New moon and sabbath and calling of convocation -- I cannot endure solemn assemblies with iniquity.  Your new moons and your appointed festivals my soul hates; they have become a burden to me, I am weary of bearing them.  When you stretch out your hands, I will hide my eyes from you; even though you make many prayers, I will not listen; your hands are full of blood.  Wash yourselves; make yourselves clean; remove the evil of your doings from before my eyes; cease to do evil,  learn to!
do good; seek justice, rescue the oppressed, defend the orphan, plead for the widow.
 Come now, let us argue it out, says the LORD: though your sins are like scarlet, they shall be like snow; though they are red like crimson, they shall become like wool.  If you are willing and obedient, you shall eat the good of the land;  but if you refuse and rebel, you shall be devoured by the sword; for the mouth of the LORD has spoken.