menewa, some people have already answered the question (thanks!) but here's my take:
In the OT, there are hundreds of laws; dietary laws, clothing laws, laws regarding slaves, property, etc. There are also moral laws (i.e. the ten commandments, etc.). When Jesus came, He set us free from having to obey the letter of the Mosaic Law, though we were still under then moral law of God. See Romans 7:1-6:
"Or do you not know, brothers --for I am speaking to those who know the law--that the law is binding on a person only as long as he lives? Thus a married woman is bound by law to her husband while he lives, but if her husband dies she is released from the law of marriage. Accordingly, she will be called an adulteress if she lives with another man while her husband is alive. But if her husband dies, she is free from that law, and if she marries another man she is not an adulteress.
Likewise, my brothers, you also have died to the law through the body of Christ, so that you may belong to another, to him who has been raised from the dead, in order that we may bear fruit for God. For while we were living in the flesh, our sinful passions, aroused by the law, were at work in our members to bear fruit for death. But now we are released from the law, having died to that which held us captive, so that we serve not under the old written code but in the new life of the Spirit."
Regarding homosexuality, there are two passages that I can think of off the top of my head that condemn it:
1 Corintians 6:9-10: "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."
Romans 1:24-32: "Therefore God gave them up in the lusts of their hearts to impurity, to the dishonoring of their bodies among themselves, because they exchanged the truth about God for a lie and worshiped and served the creature rather than the Creator, who is blessed forever! Amen.
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.
And since they did not see fit to acknowledge God, God gave them up to a debased mind to do what ought not to be done. They were filled with all manner of unrighteousness, evil, covetousness, malice. They are full of envy, murder, strife, deceit, maliciousness. They are gossips, slanderers, haters of God, insolent, haughty, boastful, inventors of evil, disobedient to parents, foolish, faithless, heartless, ruthless. Though they know God's decree that those who practice such things deserve to die, they not only do them but give approval to those who practice them."
The last verse alludes to my original post; homosexuality has now become something that we are forced to give approval to in today's society.
Hope that clarifies my view.