Georgia holds that sodomy is immoral. If this is not a rational basis, then all laws representing moral choices would be invalidated. Blackmun's Dissent Right to privacy is the key. Privacy does not protect only the traditional nuclear family. Privacy is protected, not for a social good, but because it includes a central part of an individual's life.
Individuals define themselves through intimate sexual relationships.
In Griswold , White accepted that the state must not insist that all sex be procreative. Yet, the Court refused to include sodomy within that protected zone.