First, let me dispell the Jesus never said anything against homosexuality.
Matthew 19:4 And he answered and said unto them, Have ye not read, that he which made them at the beginning made them male and female, 5 And said, For this cause shall a man leave father and mother, and shall cleave to his wife: and they twain shall be one flesh?
Mar 10:6 But from the beginning of creation, ‘God made them male and female.’ 7 ‘Therefore a man shall leave his father and mother and hold fast to his wife, 8 and the two shall become one flesh.’ So they are no longer two but one flesh.
Jesus clearly says that from the beginning male and female, husband and wife, that’s pretty clear. Liberals will tell you that Jesus would have had no concept of two gay people living in a committed relationship, that is wrong. If we consider that train of thought, which other teaching by Jesus should be discarded as old fashioned?
Mat 15:19 For out of the heart proceed evil thoughts, murders, adulteries, fornications, thefts, false witness, blasphemies:
The Greek word for fornications is porneia, from which we get pornography, which means sex related sins. Still under the law of Moses, homosexuality would have been included in this.
Now as to the Law. The function of the Law was not to save the Jews, they were saved by faith in God, just as we are. The law was to be obeyed out of devotion to God, just as we are to complete works of compassion to others and service to God. The law kept the Jews a distinct ethnic group throughout ancient history as a starting point for the Messiah. Look at all the racial groups of the OT, they are all gone, intermarried, migrated, mixed religions and customs together, but not the Jews. God used the law to keep them together for Jesus ministry. Shortly after that, 70 AD they were scattered around the world. However, their religion and customs kept them a distinct group until the late 1940s when Israel was reestablished fulfilling OT prophecy.
Isaih 66:7 Have you ever heard of a woman who gave birth to a child before having labor pains? 8 Who ever heard of such a thing or imagined it could happen? Can a nation be born in a day or come to life in a second? Jerusalem is like a mother who gave birth to her children as soon as she was in labor.
This one is a little long, but stick with it.
Ezekial 37:1 Some time later, I felt the LORD’s power take control of me, and his Spirit carried me to a valley full of bones.
7 I did what the LORD said, but before I finished speaking, I heard a rattling noise. The bones were coming together! 8 I saw muscles and skin cover the bones, but they had no life in them. :9 The LORD said: Ezekiel, now say to the wind, “The LORD God commands you to blow from every direction and to breathe life into these dead bodies, so they can live again.” 10 As soon as I said this, the wind blew among the bodies, and they came back to life! They all stood up, and there were enough to make a large army. 11 The LORD said: Ezekiel, the people of Israel are like dead bones. They complain that they are dried up and that they have no hope for the future. 12 So tell them, "I, the LORD God, promise to open your graves and set you free. I will bring you back to Israel, 13 and when that happens, you will realize that I am the LORD.
In Acts 15:20 the church leaders decided that Gentiles would not have to follow the Law of Moses and gave them only a few cultural commandments. As for Jewish Christians, I don’t know if they are expected to follow the Law of Moses or not.