The right to own property
The right to say and believe what you want
The right of self-defense and to be armed for that end
the right of privacy and security in one's home and person
The rights enumerated in the 5th and 6th amendments
Everyone, homosexual or not, already has these rights.
And finally, the right to be left alone by the government and society when one's actions cannot be proven empirically in a court of law to do harm to someone's physical well-being or property.
This one is a little vague - already people, no matter what their sex acts, are extremely bothered and harassed by intrusive laws; it's a huge topic. So this one is problematic. But homosexuals use this one to justify cruising in public parks, bathrooms, and beaches. If they want to do stuff in private, no one would even know to be able to care. But when they have anonymous sex and accost people (even adolescents) in public places, this is not a right, nor should it be.