And yet there is no evidence of this "rampant homosexuality." I'm sure that, like any big city (well "big" for that time and place), there was a fair share of shady characters, including pimps and prostitutes of both sexes. But nothing indicates that they were a bigger problem than in any other city. In fact, they are not even mentioned.
What is mentioned is the obsessive concern of the king of Sodom for money and property, and the rage of the citizenry which turned people concerned about an apparent breach of political courtesy into a mob intent on "interrogating" the offenders violently and shamefully. (See Genesis 13 & 19) These themes are picked up on in the later books of the Old Testament, especially in Ezekiel, but there is still no mention of "rampant homosexuality." Nor in the new Testament, with the possible exception of Jude. However, there are other ways to understand "heteras sarkos" and "going after" is not the same as "lusting after." And Jude should be read alongside 2 Peter, which parallels it closely. 2 Peter does accuse the false teachers that he threatens with the same punishment as Sodom of immoral practices, but it is fairly clear from the context, that the sexual immorality that he implies they are guilty of is a metaphor for turning away from the true Gospel, just as it was with Israel and Judah when the Old Testament prophets spoke of their infidelities.