Yes, the play on the phrase "Jesus and the woman caught in adultery" was intentional. So, how are we to act towards those that relate to us they have same-sex attraction? I am glad you asked!
What did Jesus do when the woman caught in the act of adultery was presented before Him? Realize, this is an account of opposite sex attraction that was acted upon.
But Jesus went to the Mount of Olives. Early in the morning he came to the temple courts again. All the people came to him, and he sat down and began to teach them. The experts in the law and the Pharisees brought a woman who had been caught committing adultery. They made her stand in front of them and said to Jesus, "Teacher, this woman was caught in the very act of adultery. In the law Moses commanded us to stone to death such women. What then do you say?" (Now they were asking this in an attempt to trap him, so that they could bring charges against him.) Jesus bent down and wrote on the ground with his finger. When they persisted in asking him, he stood up straight and replied, "Whoever among you is guiltless may be the first to throw a stone at her." Then he bent over again and wrote on the ground. Now when they heard this, they began to drift away one at a time, starting with the older ones, until Jesus was left alone with the woman standing before him. Jesus stood up straight and said to her, "Woman, where are they? Did no one condemn you?" She replied, "No one, Lord." And Jesus said, "I do not condemn you either. Go, and from now on do not sin any more."] (John. 8:1-11 NET)
Jesus welcomed without judgment, accepted without condition, and forgave without limit. I believe Jesus would do the same for same-sex attraction as He did for this case of opposite-sex attraction (Psalms 103:13,14. Romans 2:4. ).
Now all the tax collectors and sinners were coming to hear him. But the Pharisees and the experts in the law were complaining, "This man welcomes sinners and eats with them." So Jesus told them this parable: "Which one of you, if he has a hundred sheep and loses one of them, would not leave the ninety-nine in the open pasture and go look for the one that is lost until he finds it? Then when he has found it, he places it on his shoulders, rejoicing. Returning home, he calls together his friends and neighbors, telling them, 'Rejoice with me, because I have found my sheep that was lost.' I tell you, in the same way there will be more joy in heaven over one sinner who repents than over ninety-nine righteous people who have no need to repent. (Luke 15:1-7 NET)
Jesus demonstrated that we are to communicate, through our words and actions, that we would rather have this version of you in our life than to not have you in it at all. That is, we are to welcome without judgment, accept without condition, and forgive others (and yourself) without limit. Grace giving mercy (1) in compassion!
She replied, "No one, Lord." And Jesus said, "I do not condemn you either. Go, and from now on do not sin any more."] (John. 8:11 NET)
After this Jesus found him at the temple and said to him, "Look, you have become well. Don't sin any more, lest anything worse happen to you." (John 5:14 NET)
Nevertheless, Jesus full of grace and truth called sin, sin and He did not excuse, condone, or affirm it. This included sexual sins (1).
For the law was given through Moses, but grace and truth (1) came about through Jesus Christ. (John 1:17 NET)
Realize, the Bible is very clear that being tempted is not a sin but rather we sin when we chose to continually think about the sin. If we continue to think on the temptation, then we will ultimately follow through and commit sin. (2)
So, what does a happily married opposite-sex attracted male do when tempted sexually by someone of the opposite sex? They resist that temptation! Why? Because they have made a covenant with their wives before a Holy God that they will not have any other female as their partner in life (including sex partner) until death do they part. Realize, sex is only permitted within the confines of marriage and marriage is defined as between one male and one female in the Bible.
What about a single opposite-sex attracted male who is tempted sexually? Resist the temptation! Why? Because sex is only permitted within the confines of marriage and marriage is defined as between one male and one female in the Bible.
So, what should a person who is attracted sexually to the same sex do? Resist the temptation! Why? Because sex (1) is only permitted within the confines of marriage and marriage is defined as between one male and one female in the Bible. (Matthew 19:4-6, Genesis 2:24)
Yes, that was the same answer in all three scenarios. Simple answer, yet hard to live out! Yes, it can be an arduous struggle resisting an addiction, but freedom from that cycle of death is well worth the effort. Simple yet hard. Die to live, decrease to increase, give up to gain. Such are the ways of the Kingdom of God. Such is life walking in the Spirit. (2)
(1) Left click on the underlined phrase to open another article in a different tab with more explanation.
(2) The following links cover how to resist temptation in detail: