Works for me.
Marriage is sanctified by the Lord, right? So, the assumption walking into it is that it is something the Lord has given the couple.
Heterosexual couple, so even if someone commits adultery, they are not set free of the marriage. The act of adultery does not demand end-of-marriage. Even Jesus said that divorce was acceptable in that situation because of the hardness of man's heart. Not because that's what the Lord demands.
So what happens after adultery? Does the adulterer repent? (Note title of thread, and this was always about repentance. And, just so you know, that is why I kept not getting what you wanted to know.) If she/he does, then the Lord will forgive. If the spouse is born-again too, (which should be a given for a sanctified marriage, but isn't always), then there should be, ultimately, forgiveness too. And that ain't easy and doesn't happen over night, unless the Lord does a miracle.
But then something big was broken in that marriage. Trust. Trust has to be earned back. And, if it is over in the spouse's mind, there is no way of staying married. Both have to agree to stay together and no one can force anyone into staying together. So, with a heterosexual marriage, even adultery isn't just one issue. It's two issues -- the adultery itself and the trust. But, again, ultimately God sanctifies the marriage.
What is different between a heterosexual marriage and a homosexual marriage? God said clearly homosexuality is sin. He's never ever going to sanctify a homosexual marriage. It's not a real marriage, even if the government considers it one. It's not a real marriage, because God says it isn't.
And, you eluded to, in your OP, that all homosexuals have to do is abstain from sex. I disagree. Jesus said that even lusting is sin, so sin isn't merely action, but thought. Romans 1 says God gives sinners over to homosexuality because of the hardness of their hearts. God actually hardens their hearts more. So, what I would counsel a homosexual, once the person is born again would be to pray for the Lords help in softening their heart again, and good Christian counseling to learn how to live as a heterosexual. It is doable. I know of a ministry that helps people with all kinds of sexual sins, including homosexuality. (And including pornography and adultery, because, at least they get sexual sin is just that -- sin. It doesn't matter exactly which sexual sin is happening, it matters on how to stop it from happening for our sake and our love of the Lord.)
Sin is never okay.