The story of Sodom & Gomorrah is from Genesis and does not require jumping ahead hundreds of years to the prophet Ezekiel to understand their sin or the consequences. The complete story can be found in Genesis 19: they were perverts engaged in homosexuality and seeking to rape God's angels sent there to save Lot and his family. The text is very clear and unambiguous. God punished those wicked people by raining fire & brimstone down upon them from the sky. I believe archaeological evidence has been found to confirm the story.
No amount of deception, obfuscation, and lying can hide these clear facts from scripture. And if there were any doubts that homosexuality was a sin for all time, one only needs to read Romans 1 to see it condemned as such in no uncertain terms and with clear context.
One is saved by repenting from sin (turning away from it) not embracing it and by believing in Jesus Christ. There is no other way to escape the consequences of sin which is eternal damnation in hell. For anyone truly wanting to understand these realities, read the entire book of Romans. It is filled with great wisdom about these facts and much more.
Psalm 119:36