The question arises about the position of people of homosexual orientation before God. Gays and lesbians are the same as heterosexuals--we are all sinners before God, and we all require salvation to live in communion with him. Sexual orientation is not the dividing line. Sexual behavior is. Sex is not essential to life and you can live without it. Many of us should. If you are not married, you should not be engaging in sex. Yes, heterosexual as well as homosexual sex is forbidden when the participants are not married.
There are a number of passages that denounce the practice of homosexual behavior. They seem vague and non-specific to a litigious generation. In Leviticus 20:13 the Bible says that man must not lie with a man as with a woman. That is pretty specific and non-ambiguous. Some people want to exclude Old Testament passages because they say you must take all the Levitical Law or none of it. I don't know that I agree. Jesus took some and not all. Paul in Romans 1:26-27 warns against all same-sex practices. Defenders of the practice claim that only one passage in New Testament condemns homosexuality, and gays and lesbians should be able to marry in the same manner as heterosexuals. The defenders claim their civil rights are being violated, and their opportunity to experience a full life is curtailed. I'm not convinced that God is concerned with civil rights or fair play. He is concerned with salvation from sin.
The passage found in Genesis quoted above states what God approves; however, not every instruction applies to everybody. Paul in Ephesians says you may marry or stay single. There are people in the Bible whom God did not permit to marry. Some traditions, like multiple wives, were tolerated for a while, but eventually abandoned. If the Bible is not specific in forbidding homosexual marriage, it certainly never approves it.
Nothing in the Ten Commandments or the teachings of Jesus implies that we should expect to be happy and content. Homosexuals and heterosexuals are equally commanded to be obedient, to love the neighbor, to live righteously, and to confess their sins. If these commands limit human happiness, so be it. Marriage is between men and women. Other practices are not approved by God. I can't see the value of saying that we might get away with it since there is only one direct and specific prohibition against it in the New Testament. I think it is presumptuous to assume things to be the way I want just because it will make me happy. God is not concerned with my happiness, but my salvation. King Saul experienced the consequences of acting presumptuously before God. It cost him his sanity, the Kingdom, and eventually his life.
There are considerable risks to rewriting the Bible!