The question is, what should a person do if they have same-sex attractions and they want to try to live a chaste life in accord with the teachings of the magisterium. This is one that I did some research on, and I'd like to express my indebtedness to Ron Belgau and Eve Tushnet (Eve has a blog that is definitely worth a look) for insights that I've pillaged from their writings.
Basically, I think that there are three basic psychological needs which are fulfilled through sex and family life in the case of married people. These are creativity, communion and self-giving. If a celibate person does not find a way to express these elements of personality in other ways, they will find themselves inevitable, and perhaps compulsively drawn to sex as a means of assuaging the hunger. Eve observes that you need to develop a strong relationship with artistic beauty, and I would add that for most people having a creative outlet is essential. Also, as Socrates observes, the road to Truth is very often, perhaps most often, via the Beautiful. The need for communion has to be fulfilled through strong friendships, same-sex friendships in particular in the case of queer people. Same-sex attraction, at least in my mind, is constituted by a disordered sexualization of an ordered desire for close communion with members of one's own sex. Finally, the role of self-giving is essential. John Paul II relates masculinity and femininity, in their most essential forms, to fatherhood and motherhood – and points out that these elements of personality can be expressed spiritually by those who are not biological parents. People who wish to live a celibate life need to make some sort of corporal work of mercy a major part of their spirituality. I would add that works which concentrate on ministering to the needs of those who are deeply lonely, outcast, alienated or ostracized by society is probably a good idea for LGBTQ folks, because let's face it, most of us have a pretty deep experience of alienation ourselves. Eve references prison ministry. I personally did ministry to the homeless. I would also add that AIDS hospices are desperately in need of volunteers, and that Catholic outreach in this area is lacking, to say that least.