A common enough question; let me take the questioner on, even more directly than other answers one may hear. The hubris, the beam-in-the-eye, the inattention to Christ’s message of love the sinner, for starters, all ask the questioner to kneel before GOD with a broken and contrite heart, confess his or her own sinful nature, and rise forgiven but still humble.
Sodom and Gomorrah? That wasn’t homosexual so much as a ritual humiliation. Their ‘sin’ in fact was to humiliate the foreigner who came inside their gates for a night’s protection. In those times, the protection of a walled city was sacred. I repeat, sacred. The profanity of humiliating an innocent traveler was paramount, and Abraham’s failure to find any righteous men in that town was its doom.
Leviticus? As pointed out in other places, many sins in that text occur today without a second thought. One of them is a social taboo, and the others? Why does the one act like a splinter on the handrail, and pierce the skin, while the rest have been worn to a patina and slide by unnoticed? Who remembers the passage in full? Who can even find it?
Then we come to Paul and Jesus. Jesus’s recorded words do NOT mention same-gender sexual relations. Paul’s do; Paul also makes the point of confessing, with regards to living a celibate life, that celibate is better but only in his opinion, not GOD’s. Expressing disgust at others failing to remain celibate when marriage wasn’t on the table? Paul said it, but did GOD?
Finally, we land on the inerrancy of Scripture – is it either word-for-word GOD’s love letter and GOD’s admonition, or ancient phantasies blowing in the wind, with no middle ground? How dare we take GOD’s word to such a ridiculous place!
Genesis has GOD’s fingerprints all over it – but it is also founded on an origin story, Abraham’s tribe’s origin story. The ancient world abounds in them. The New World, e.g. Inuit and AmerIndian, have a rich variety of their own. None of them, Abraham’s included, bear any factual relationship to the world we inhabit. Saying that Abraham’s is science is beyond ludicrous. Instead, GOD’s fingerprints on that origin story mean that GOD chose Abraham, and infused His love and forgiveness, His patience and promise, His redemption, into the material He started with.
GOD created the world – 13.78 billion years ago not 6,000. GOD saved the world, 1989 years ago, in 30 CE. GOD doesn’t pettifog over personal distinctions. GOD doesn’t like heterosexual betrayals, nor presumably homosexual betrayals. But GOD Ab So Lute Ly does not (speaking for myself, not GOD) hold any sin to be worse than any other, save rejecting the Holy Spirit. Accepting grace is a one-and-done deal, no going back.
Being created with homosexual orientation is not a choice, and more than pederasty. We understand the deep and permanent emotional scarring of that, so have no patience with adults who sexually abuse children. But adults who come to each other in a committed bond that involves sexual union are nobody’s target, except for people who do not understand what GOD demands of them. To persecute homosexuals is to adopt the hypocritical sheep’s clothing of “Christian” while operating as a wolf of hatred.
It’s that simple.