It's such a stupid argument that Jesus was silent on sodomy. He called out 'sexual immorality' and he quoted Leviticus which means he considered it authoritative. It's dishonest to say that Jesus defined 'sexual immorality' any way other than how the Old Testament defines it
He did speak on homosexuality, just not in the way that you would expect:
“For there are eunuchs who are born thus from their mothers womb, and there are eunuchs who are made eunuchs by men, and there are eunuchs who are eunuchs for the kingdom of heavens sake. Let those who can accept it, accept it.” Matthew 19:12.
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Context of the Terms Used:
Here, Jesus refers to three exceptions to the requirement for heterosexual matrimony, all “eunuchs.” What are “eunuchs?” Eunuchs were highly ranked, but socially “deviant” men in charge of protecting and caring for female royalty. To be best at being a eunuch, one could never slip into a relationship with one of the female heirs, for all in the kingdom’s lineage could be compromised. Biblical historians speak of how eunuchs had many feminine, emasculate qualities, which societies back then detested for these men had little to no interest in sexual relations with females. While this was a very different zeitgeist than now, one can see a correlation between how eunuchs were seen and how gay males are seen by society.
In this passage, Jesus Christ list three exceptions to the command for Christians to engage in heterosexual matrimony:
(1) eunuchs born that way;
(2) eunuchs made that way by man;
(3) eunuchs who promise their lives to God.
Castration was a common practice among eunuchs. While many people believed that all these non-virile men were castrated, various biblical dictionaries go into detail on how castration was not the only way to become a eunuch.
Here, Jesus first says “eunuchs born that way” are exempt from heterosexual marriage. Since eunuchs are supposed not have “relations” with female heirs, and these eunuchs were born without attraction to woman, gays, bisexuals, and lesbians should use Jesus Christ’s exemption of “innate eunuchs” from heterosexual matrimony to speak for all gay people. In essence, here,
Jesus Christ tells his disciples that people born without the innate attraction to the opposite sex should not marry people of the opposite sex."
http://www.religioustolerance.org/ashford03.htm
Back then, "eunuch" was a broad category for any gender-variant male. It would've included effeminate gay men as well as what we'd call transgender/transsexual women and third gender people.
The centurion who asked Jesus to heal his servant was probably in a sexual relationship with him, as well.