Well apparently that was an epic fail on the part of Jehovah, because there’s still some Lesbians, Gays, Transsexuals and Bisexuals around…
As already noted by another in their response, Ezekiel didn’t seem to see sexual sin as chief among the problems with the residents of Sodom.
Furthermore, the development of stories in that period of Bible history was highly interpretive - the narrative was intended to explain why things are the way they are. God rewarded good and He punished iniquity. Sodom was destroyed, so the people of Sodom must have been VERY bad. It is likely that the whole story about the attempted rape of the angels grew out of this storytelling paradigm.
It is worth noting that there is a perfectly natural (though albeit, uncommon) explanation for the destruction of Sodom and the surrounding cities. There is a very telling clue in the story about Abraham pursuing the men who raided Sodom and carried off Lot and his family - the valley was full of tar pits, into which some of the men fell and died.
These tar pits would seem to be a marker of the geological phenomenon that actually destroyed the cities a short time later - a seismic event that triggered the release and combustion of a large petroleum deposit.