My answer of course was no because at that moment I wasn't disgusted by the sin of the individual, but by the individual, and there is a difference. So during the course of our interaction with each other I began to ask myself how then would Christ have responded?
My answer is that Jesus engaged with the people of his culture, all of the people, including the ones considered sexually immoral. We see numerous examples of this throughout the New Testament, but some of his more popular interactions are with the sinful woman (Luke 7:36-50); the woman at the well (John 4:13-26); and the woman caught in adultery (John 8: 3-11).
So over the course of our interaction together, my heart began to change and instead of looking on the individual with judgement and disgust, I started to see them through the lens of the love of Christ. I was then saddened and disgusted at the sin in their life because of their individual choices; but I had complete love for this individual as my desire was and is to see them freed from the bondage of all sin in their life. Instead of continuing to have a heart of judgement towards this person I prayed for them that their eyes would be open and that they could be released from the power and penalty of sin.
My point in sharing this is because I believe that my initial response is the initial response of many within the church, which doesn't display an attitude of love towards others. I once heard a Pastor proclaim in front of his congregation how disgusted he was of gays and lesbians and his lack of desire to interact with them. This is not the right response and I called this pastor out in love and to my knowledge he repented of his actions.
Instead of judging these individuals and condemning them, we should instead be loving them toward Jesus. A relationship with Jesus is the only hope for people who are caught in their own ways. Typically there are two groups when it comes to sexual sin, the permissive and the judgmental, but instead we should point all people to Jesus and the gospel as in and through him only true transformation can take place.