Common sense and logic. Being gay harms no one, in fact, the belief that homosexuality is a sin actually causes harm in and of itself. So, if anything is immoral here, it is the belief that homosexuality is wrong, not being gay.
There's a difference of opinion on that.
Homosexual sin - No harm?
First, "gay pride" (two sins). They flaunt it in our faces and try to legitimize it. You don't hear of "adultery pride" parades or "necrophilia pride" parades do you? But even if there were we'd take an equally stellar stance against those. We don't want to hear about it.
Second, most homosexuals who claim to be Christian try to persuade others it's not a sin, leading many (many) into perdition. We don't want to see even one soul lost.
Third, most homosexuals distort the scriptures in some fashion or another in order to try to justify their sin. The distort who Jesus is (saying he's not God so he never spoke out against gay sex sin); they make lengthly arguments against Leviticus, Romans 1:26-27, I Corinthians 6:9-10, etc. Generally, they attack the Word of God and thus attack God himself. We defend the Word and God.
Fourth: Sin is a reproach to individuals and nations and brings God's disfavor on men and nations. Read Deuteronomy chapter 28 to see the curses of disobedience.
Fifth, they attack the Sons and Daughters of God when we stand up for the truth of God's Word. They call us bigots, homophobes, and all manner of names because we disagree with their stance.
Sixth, they push their illicit agenda into every corner of America. Suing the Boy Scouts and anyone else who disagrees with them. They try and sometimes succeed in pushing their gay agenda in elementary schools and elsewhere where it doesn't belong. Nine year old children shouldn't have to hear that Billy's daddy is doing another guy, or that it's ok to do it. They push their agenda in our faces until we're quite sick of it. We don't need to know which way people perform sex acts.
Seventh: (need I go on?) They (and heterosexual sinners) cost taxpayers untold billions in unnecessary health care costs to treat AIDS and other diseases they give to each other. It costs us all money out of our pockets.
And eighth: They refuse to repent of it, making their own salvation and those who they lead astray a serious question mark.
And there's more but that's for starters.