Here is a dvar Torah on parsha Vayera Bereshit/Genesis 18.1-22.24 which is the parsha that includes the story of Sodom & Gomorrah.

You should read the whole dvar Torah if you are interested, I found it to be good. But here are some choice excerpts about the sin of Sodom & Gomorrah - they were cruel and selfish, and inhospitable to guests and the poor & less fortunate. One can find common parallels with modern USA cruelty today. I wrote a huge cracked out essay about this on Hexbear once but I can’t find it, I’ll link it if I do.

In our contemporary lexicon, the phrase “Sodom and Gomorrah” has become synonymous with extreme depravity and immorality, with a particularly sexual connotation. Within the narrative in Bereshit it would seem that sexual immorality is only part of the evil of Sodom. Contrary to popular usage it is also clear from the reading of the narrative that it is not homosexuality that is the sin of Sodom and Gomorrah (though Jerry Falwell and others might disagree).

The people of Sodom did demand that Lot (Abraham and Sarah’s nephew) hand over the strangers in their house (actually messengers of God sent to tell Lot of the impending doom) so that “we may know them,” which is clearly a sexual reference in terms of biblical Hebrew. However, what makes them sinful according to our Sages is not sexual desire or lust, but rather their desire to abuse and humiliate other human beings because they are strangers in their midst. The two messengers could just has easily have been women and the people’s response would have been the same.

The Sages teach us that only the wealthy were welcome as guests in Sodom. The poor were to be expelled or killed.

In his book of Torah commentary Jewish Values in an Open Society, the economist and business ethicist Meir Tamari writes about the sin of Sodom and Gomorrah as the sin of “Economic Egoism.” He reminds us that according to our Sages the greed and desire for wealth on the part of the residents was insatiable. Anyone who got in their way, such as a poor person who might ask for some of their money or food, was expendable. All common human decencies were anathema to the Sodomites.

Part of the context for this is that there is a narrative over a few chapters in Genesis of Sodom and Gomorrah being the people everybody hates, objectionable both to their peers and to the divine observer. Abraham is the figure showing mercy and haggles with God to spare them if 50 (or 20, or even 10) righteous people can be found), and it is implied that not a single one is found.

The ultimatums and threats made to Lot can more accurately be seen as sexual assault, as well as a violation of the cultural norm of hospitality to guests. Relevant to part of your question is that Lot, as the protagonist, does not see it as transgressive to give his already-betrothed (!) daughters over to his neighbors. To keep the story concise it would have made sense to give just one last particularly shocking offense before the resolution.

Like with the rest of the Torah, the story was crafted in a certain social/historical context, passed down orally for generations, and then written down by multiple people trying to portray it coherently for the ages. It works nicely as an origin and identity story, but it breaks down if you nit-pick it, especially if you’re reading it in a modern Indo-European language. And vernacular nit-picking is what a lot of Protestants have made it their business to do.