There are 3 forms of Transparency that give someone, who is attracted to the same sex, a godly, healthy intimacy with the same sex that I'm sure they desire. That is Spiritual Transparency, Emotional Transparency, and Physical Transparency.
1. Spiritual Transparency - Being vulnerable with one's spiritual state with another human in regards to their love for Christ, their love for Church, and the calling to fulfill the Great Commission. Also, being vulnerable with one's sin struggle and growth in their faith in the sanctifying work of Christ in their life.
2. Emotional Transparency - Being vulnerable with one's emotional state with another human in regards to their life's goals, joys, losses, insecurities, desires, etc. We should also be okay with crying, communicating what is deeply troubling our hearts, and relying on others to love us and accept the gift that they like us and want to be with us. Looking at someone and expressing your emotions during a time of joy, sadness, pain, and relief is an amazing experience.
3. Physical Transparency - Physical Transparency is underestimated in so many ways in our society right now, especially within the Christian Church. In the non-Christian world, sex is usually used to experience a sense of physical transparency. Now I'm not going to dive into my Christian worldview and its beliefs about how sex outside of God's creativity is not a true form of physical transparency, that is a different topic.
Since the Christian community is unchanging on sex before marriage and so forth, there isn't much context for Christians to experience a a time in which they experience each other physically in a non sexual way. What I mean by this is knowing someone physically. The Church is good at knowing each other emotionally and spiritually, but we forget we are also physical beings and we ignore the "knowing each other physically part." Here is an interesting example, I have friends that have played sports in high school and at Biola, and they play sports that involve physical contact and physical reliability to accomplish a win for the team. They know who runs the fastest, who is the strongest, and who is in the best shape. They also see each other naked in the locker room and other places in which physical nakedness or Transparency takes place. They know who has the biggest penis, smallest penis, who is uncircumcised and who is. This physical nakedness brings a bonding that males benefit from, such as acceptance with one's body, not comparing and judging, and being confident with the body and body parts you have. With porn today displaying only big penises, men now believe they need to be "big" in order to be a man or please a women, which is not always true.
THE LOCKER ROOM
I will dive more into the physical transparent idea because I know this can get very controversial, especially within the church. But overall my main point is this, I believe every man needs to experience the naked Locker Room scene in order to know they are a man and have the same body as every other man. They don't need to experience shame for having a body or for having a small or uncircumcised penis, and someone who experiences same sex attraction needs to be given the opportunity to be in this environment to train themselves to not lust after their male buddies but see them as they fully are, their brothers in Christ that have a male body. Because here is the situation you are going to run into, these christian men who struggle with same sex attraction have an attraction to the male body, I don't necessarily believe that is an intrinsic sin, but they find the male body to be a beautiful and interesting art work from God. And just like an artist who wants to see a beautiful piece of art and can't be satisfied until he sees the art, that is how I think men who struggle with this need to experience their male buddies, they need to see them physically (in the proper context) and understand that they are just that, their Christian male buddies who love them. (I also think these applies to everyone, not just those that are attracted to the same sex)
Here is what I think is an extremely cool video concerning Physical Transparency and how it is tied to a person's being