I am not going to type all 9 times wherein the specific Sodom and Gomorrha are used... I will type the first time so one can get the idea.
Matthew 10:15 Verily I say unto you, (the you are the newly elected twelve of verse 2-4) It shall be more tolerable for the land of Sodom and Gomorrha in the day of judgment, than for that city.
Now of course the whole chapter 10 needs be read to get the fullness of the instruction given... But Christ left no doubt that Sodom and Gomorrha would yet again be practiced. So He forewarned the individual and the nations to expect their judgment to be greater than was the judgment on the first Sodom and Gomorrha.
It really does not matter what people are comfortable in denouncing, it is what the judgment promised to the participants and the onlookers that cheer, legislate, and make like evil is good and good is evil. They are going to get theirs. To say such things is politically and even religiously incorrect, regardless of the warning in advance.
Most (I think all but one) of the references in the NT to S&G do not specifically reference their sexual sin, but rather are used to describe the severity of punishment others will receive for sins that have little or nothing sexual in nature, such as rejecting the word of Christ.
IOW, the references are used not to reinforce the idea that homosexual sin is more sinful than other types of sexual sin, but rather as an illustration of severity of punishment.