I am neither religious nor gay, but I am very interested in religious studies, and what you describe sounds very similar to me to what I have read regarding liberation theology. While liberation theology is most known as a theology of and for the poor and oppressed, it also is intimately concerned with social systems of inclusion and exclusion in the context of the Christian faith. For example, the concept of purity and impurity in relation to people, what it means to be created in the image of God, and the relationship between Christians and the social underclasses of different societies and cultures. Historically and internationally, there are clear similarities with LGBT persons and the very poor in terms of social labeling and status. Tomes are written on God's relationship to those rejected by society. In a time long ago, when I was a religious Catholic, my favorite verse was always Matthew 25:31-46, in which God intimately identifies with the poor and mistreated. It still brings joy to my heart to see a Jesuit as Pope in Rome.