Yes.
It is true that Jesus never named homosexuality specifically but neither did He specifically name rape or incest or wife-beating. We wouldn’t therefore argue that they are holy acts.
It is the teaching of the Bible itself, and has been the belief of Christians throughout the ages, that the Bible is inspired by God. And Jesus is God. Therefore, Jesus inspired the passages that directly condemn homosexual acts.
At the very least, we would say that Jesus was 100% in agreement with the God-inspired teachings of the Old Testament.
Matthew 5:17-20
17 ‘Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfil them. 18 For truly I tell you, until heaven and earth disappear, not the smallest letter, not the least stroke of a pen, will by any means disappear from the Law until everything is accomplished. 19 Therefore anyone who sets aside one of the least of these commands and teaches others accordingly will be called least in the kingdom of heaven, but whoever practises and teaches these commands will be called great in the kingdom of heaven. 20 For I tell you that unless your righteousness surpasses that of the Pharisees and the teachers of the law, you will certainly not enter the kingdom of heaven.
Jesus not only gave His support to every detail of the law, He said that those who’s righteousness did not surpass that of the Pharisees and the teachers of the law will certainly (note the emphasis) not enter the Kingdom of heaven.
No one can read this chapter and conclude that Jesus was lowering the bar. Rather, He challenged the loose interpretations of the Pharisees who said, “Oh yes, but it doesn’t really mean such-and-such. What it is really referring to is such-and-such and therefore we can…”
Those are exactly the arguments used by people today who want to reinterpret the Bible to allow homosexuality. More biblical Christians are often accused of being “Pharisaic”. We have to question however if it is the other way around. The Pharisees, while clearly being rules-based and loading burdens on others, had a loose interpretation of the law and sophisticated ways of avoiding it.
By strongly upholding the law, Jesus upheld what it says about homosexual acts.
As we saw in the question “Are there other relevant passages?”, the word “porneia” originally referred to prostitution but became an umbrella word for “sexual immorality” in its various forms. Therefore, when Jesus talked about porneia, He included homosexuality. His hearers understood Him to be referring to those sexual practices prohibited in the Law.
Mark 7:14-23
14 Again Jesus called the crowd to him and said, ‘Listen to me, everyone, and understand this. 15 Nothing outside a person can defile them by going into them. Rather, it is what comes out of a person that defiles them.’
17 After he had left the crowd and entered the house, his disciples asked him about this parable. 18 ‘Are you so dull?’ he asked. ‘Don’t you see that nothing that enters a person from the outside can defile them? 19 For it doesn’t go into their heart but into their stomach, and then out of the body.’ (In saying this, Jesus declared all foods clean.)
20 He went on: ‘What comes out of a person is what defiles them. 21 For it is from within, out of a person’s heart, that evil thoughts come – sexual immorality, theft, murder, 22 adultery, greed, malice, deceit, lewdness, envy, slander, arrogance and folly. 23 All these evils come from inside and defile a person.’
According to Jesus, sexual immorality defiles. See also the parallel passage in Matthew 15:16-20
Matthew 19:3-6
3 Some Pharisees came to him to test him. They asked, ‘Is it lawful for a man to divorce his wife for any and every reason?’
4 ‘Haven’t you read,’ he replied, ‘that at the beginning the Creator “made them male and female,” 5 and said, “For this reason a man will leave his father and mother and be united to his wife, and the two will become one flesh”? 6 So they are no longer two, but one flesh. Therefore what God has joined together, let no one separate.’
Homosexuality was considered sinful by the Jews of Jesus day. See Preston Sprinkle’s talk, “Jesus Was a Jew: Understanding Jesus and Same-Sex Marriages in His 1st Century Jewish (Not Our 21st Century Western) Context”. If Jesus had intended to challenge that attitude, He clearly would have addressed it specifically. He didn’t identify homosexuality because everybody already understood that is was wrong. That didn’t need stressing.