I guess the same reason any sinner thinks they are going to heaven: Repentence.
Of course, that does involve using the power of the Atonement to give up your sins.
It is so easy to get caught up in the wrong responses on this topic. Some seem to be afraid to believe that a gay person can actually be saved. Being gay is not a sin, any more than being heterosexual is a sin. It is the lifestyle that one lives that makes opne a sinner or not. We all sin. As the Bible says, "all have sinned and come short of the glory of God." The key, as you said, is repentence.
No drunkard shall enter heaven, but there will be many who were actually recovering, or non-drinking alcoholics who will be there. The difference, a drunkard is active in his alcoholoism, and a recovering alcoholic has chosen not to drink. I would also say that there are even people who drink, but do not get drunk (social, ocassional drinkers), who can be saved.
Even as believers, we still find ourselves involved in sin from time to time. It is not, however, what we do on a regular basis just because we can. Jesus gives a life of joy, and in most cases people who live their lives to sin do not have joy. They may be happy with themselves, but that joy that flows within a true believer cannot happen in someone who lives for their sin, or allows their sin to control them.
God bless you all