Those claiming Jesus never had anything to say about homosexuality always omit his repeated references to Sodom and Gomorrah as examples of what awaits those who do not repent. Matthew 10:15, Matthew 11:23-24, Luke 10:12, Luke 17:29.
The apostle Peter, who no doubt heard Jesus' teaching, says virtually the same thing in one of his epistles. 2 Peter 2:5-7
And no, Sodom and Gomorrah were not destroyed for the sin of "inhospitality." Everyone in Jesus' time knew what Sodom and Gomorrah were about:
". . .Sodom and Gomorrah and the surrounding towns gave themselves up to sexual immorality and perversion. They serve as an example of those who suffer the punishment of eternal fire." Jude 1:7
Jesus mentions this fate more often than just Matt and Luke. He advises that this fate, for those who won't receive His Word, in Mark and John and numerous other books, as a fate worse than the homosexuals received, as a fate worse than death.