Anyone can practice Krishna consciousness. Chanting Hare Krishna mantra, reading Srila Prabhupada's books, coming to the temple, taking prasadam are open to everyone...and spiritual advancement will certainly be the result.
Initiation is a very serious commitment however, and occurs only after a good deal of self-reflection and training. First, the candidate needs to seriously practice Krishna consciousness for six months at the very least. This involves studying Srila Prabhupada's books, demonstrating practical knowledge of the philosophy of Krishna Consciousness, associating with devotees, following the four regulative principles and chanting sixteen rounds of Hare Krishna mantra on beads daily. The four regulative principles are: No meat eating, no gambling, no intoxication and no sexual connection outside of marriage, except for the procreation of children.
Once you have been doing the above for some time—six months at the very least—you can approach a senior member of ISKCON and request to be initiated. The prospective guru and aspiring disciple then get to know each other for some time—at the very least six months more. If they are both convinced that it is a workable relationship—the disciple is able to follow the regulative principles and is willing to take serious spiritual instruction from the guru—then initiation may take place. At the time of initiation, the disciple vows to follow the four regulative principles and chant sixteen rounds of Hare Krishna
One's sexual preference does not matter. However, since there is no possibility of having sex for the procreation of children within a homosexual relationship, that would mean the two persons, as initiated disciples, would have to remain sexually inactive throughout their relationship. I hope this is helpful.