I think the question should be: Do we trust Jesus as the ultimate moral source, or do we trust someone else? Someone else like our friends (gay or otherwise), the government, one church or another, or culture at large?
This is the American Church’s cultural issue of a generation - and here is what I believe Jesus has to say:
1) Homosexuality, even within marriage, is sin
‘Did God really say ___’ has its original origins in the garden; it’s pretty clear that God considers sexual relations of any significant kind sinful unless constrained within marriage between one man and one woman. There are many elements in the Bible that are descriptive, meaning they are included to describe circumstances or characters. The Sodom and Gomorrah story (as well as the details with Lot) are clearly descriptive. We are not to emulate them as they are presented, but to use the story to learn. The second type of element we encounter in Scripture is prescriptive, meaning, direct commands, encouragements, etc. Anytime Jesus says 'you have heard ___ but I say ___’, we are dealing with a prescriptive element.
There are only two prescriptive passages in the bible that pertain directly to the participants in marriage - 'Therefore a man shall leave his father and his mother and hold fast to his wife, and they shall become one flesh’, Gen 2:24, and more directly, Jesus’ clarification of marriage when questioned in the first half of Mathew 19. Jesus directly reaffirms this passage so strongly that his own disciples start to wonder if they should even get married at all. So in order to actually follow Jesus it seems like we also should personally affirm God’s original design, even though it seems extremely restrictive, and even if it excludes things like homosexuality, polygamy, pedophilia, bestiality, etc.
2) Sin is ultimately a heart issue and not a sexual issue
Let’s dissect homosexuality, because not all 'homosexuality’ is the same. Someone might say they are gay because they are attracted to the same gender. Someone else might say they are gay because they are participating in a lifestyle of homosexual relationships. It seems pretty clear that raw sexual attraction (if not to your husband/wife) is a temptation rather than a sin, no matter to whom that attraction is directed. The moral question, the sin issue, is what to do with the temptation. And speaking of temptation, if we really believe that Jesus was tempted in every way as we are and found blameless then it makes sense that he also experienced same-sex attraction and overcame it, as he did with other attractions, such as heterosexual attraction.
God’s view on temptation, sin, and on people, is the heart first and actions second. Throughout history the visible sins almost always tend to be treated as worse than others, but Jesus makes it clear that he is most concerned with the inner being: “You have heard that it was said, ‘You shall not commit adultery.’ But I tell you that anyone who looks at a woman lustfully has already committed adultery with her in his heart.” Two different people, both attracted to women, could look at the same girl and one could sin and the other not; regardless of the attracted person’s gender. Lust, or a desire to act on the temptation seems to be the distinction that Jesus really cares about even if action is never executed. If we are going to stand with Jesus, then in addition to personally affirming God’s original design for marriage, then we need to have his perspective on sin. What matters the most is not the type of sin, but what it does to a person’s heart, and therefore their relationships with God, others, and themselves.
3) God has grace for all sin through Jesus
What makes Christianity different from every other religion in the world is the Grace we have by the death of Jesus on the cross. Jesus looks at our sin (as horrible as it could be such as with a rapist or pedophile), and says 'I chose to be guilty of that before God on your behalf’. Through Jesus there will be gay people in heaven and in right relationship with God, just as there will be murderers, etc. Lets take a non-cultural sinful sexual issue as an example: polygamy. Abraham was a polygamist, and polygamy goes against the fabric of marriage as God intended it. However, Abraham had faith in God, and ultimately faith in the Jesus he didn’t know, and through that faith Abraham is credited with righteousness. He is in right relationship with God in heaven right now, not because he ceased to practice polygamy, but because he had real faith and real relationship with God. Polygamy was to his culture what homosexuality is quickly becoming to ours - a culturally acceptable sinful practice. God gives grace for sin no matter if it is acceptable to the culture at large or not, just as all sin harms our relationship with God, no matter the cultural overtones.
That means we as Christians (in addition to holding a unique definition of marriage and having a unique perspective of sin), need to have a unique response to sinful behavior. We need to have a restorative loving grace for all sinners in the same way God has had a restorative loving grace for us. Jesus made his choice to be guilty for God on our behalf while we were still guilty ourselves. I feel like this is the number one area we are not acting correctly in the church as a whole with regard to sexual sins, but to be fair, the church is a large body and has many members, all of whom are Christians in the first place because they know they are sinful and need a savior. Here is a small clip of Tim Keller on the response issue (he is a pastor I have respect for) and I think he captures the complexities better than I could; if you care to watch -https://www.youtube.com/watch?v=7dY0ZTuFGCE.