I take his vehemence in destroying these two cities as a measure of his opinion on the subject.
Elsewhere (Leviticus, I believe) it says homosexuals should be killed. I would think that clears up any lingering ambiguity regarding the topic.
And it’s not just the Old Testament. The New Testament, likewise, is clear:
“For this reason God gave them up to dishonorable passions. For their women exchanged natural relations for those that are contrary to nature; and the men likewise gave up natural relations with women and were consumed with passion for one another, men committing shameless acts with men and receiving in themselves the due penalty for their error.” (Romans 1:26-27)
“Or do you not know that the unrighteous will not inherit the kingdom of God? Do not be deceived: neither the sexually immoral, nor idolaters, nor adulterers, nor men who practice homosexuality, nor thieves, nor the greedy, nor drunkards, nor revilers, nor swindlers will inherit the kingdom of God.” (1 Corinthians 6:9-10)
“Now we know that the law is good, if one uses it lawfully, understanding this, that the law is not laid down for the just but for the lawless and disobedient, for the ungodly and sinners, for the unholy and profane, for those who strike their fathers and mothers, for murderers, the sexually immoral, men who practice homosexuality, enslavers, liars, perjurers, and whatever else is contrary to sound doctrine. . . .” (1 Timothy 1:8-10)