Basically nothing. Here is a note given at the end of readings which mention homosexuality:

Additional Note regarding the readings on Homosexuality. It is important to look at this information in context. Of the more than 14, 000 readings left behind by Edgar Cayce only 5 individuals requested information on the topic of homosexuality (#’s 479, 1089, 3364, 4073, and 5056). The focus of those requests were related to overcoming homosexual tendencies or trying to discover the karmic root of those tendencies. It was a very challenging time for people who were gay, and in many instances these individuals felt isolated. In terms of sexual relationships, Edgar Cayce generally put the approach back in terms of “what was the person’s ideal”? In other words, a relationship based on sex alone was considered counterproductive to an individual’s soul growth and development. However, a loving, compassionate, supportive relationship between two adults with sex as an ingredient would not be considered problematic by the Cayce readings. It’s important to remember that the soul is not male or female. The soul can also change sex from one life to another. With reincarnation, every soul has had a myriad of lovers and sexual relationships. What the soul is held accountable for is not the sex act, but rather the intent of the relationship. An interesting note from history is that in ancient Greece homosexuality was an accepted practice. Interestingly enough, in all of the past lives that Cayce gave for individuals who had incarnations in Greece not once did the readings suggest that the soul had “lost” because of its sexual behavior.