Well yes there is interpretation and then there is Interpretation. Let's take the "all people are made in God's image, therefore all ways people exist today are Good." Even if you take the creation story as allegory, what you see there is the initial creation was Good, but that was before the fall. And the fall wasn't "eating the apple" the fall was "putting yourself in the place of God." They will also happily say "all people in this class are created in God's image, because we like that class" but they don't say "alcoholics and gamblers are made in the image of God!"
So everything we have is a corruption of the original state. Even "hetero-normative" sexuality is corrupted. When humanity tries to play god, we inevitably get it wrong - and this includes when we try to claim we know exactly what God is saying, through scriptures or otherwise.
There's a large number of folks that don't quibble about the specifics of "oh the text meant only this type of sexual perversion, not this one, so I'm justified". In fact, the whole point of "we are OK to do this because..." is the actual debilitating sin - it's saying "we know better, we're the arbiters of what is Good and Evil, not God."
So "being" non-normative isn't the sin. Having urges and tendencies isn't a sin even. Living your life pursuing those tendencies, and thinking that they're ok just because they are the things that make you feel good about yourself and the world, without considering if those align with a general right relationship with other people and a right relationship with God, that is the sin. I believe you can be a non-heteronormative Christian just as you can be an alcoholic Christian, or a porn-addicted Christian, or even a murderous Christian. At the end of the day the question is, are you serving yourself (or the world), or are you glorifying God? Are you missing the mark?
And yes, Jesus did supposedly say that it wasn't just "acting" on things that is sinful, it's what's going on in your heart - the whole "if you think about hurting people, it's murder. If you lust after someone in your heart, it's adultery" stuff. It's hard and and it doesn't often feel good - but it's not about our feelings. A big miss on modern (especially US) Christianity is it seems to put things too much on the individual - when it's a pretty easy read of the Bible (both Old and New Testaments) to see that it's all about the glory of God and the relationship of all of humanity with God - sure you have some individual benefit, but that's a side benefit, not the main point! Jesus main message wasn't "you are individually saved" it was "the Kingdom of Heaven is here!" A kingdom is corporate, not individual.
At the end of the day you either believe there is a standard outside yourself or only inside yourself. You believe it's either absolute or it is contingent on circumstance (social, cultural, situational, doesn't matter).