WordNet records no synonym and no antonym for golden rule. It is the only member of each of its synsets, which is common for technical, taxonomic and single-sense vocabulary — there is no other English word that means the same thing. The broader and narrower terms below are the useful relations in that case.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
any important rule
“the golden rule of teaching is to be clear”
a command based on Jesus' words in the Sermon on the Mount
“Whatsoever ye would that men do unto you, do you even so unto them”
Synonyms, antonyms and the broader and narrower relations for golden rule come from Princeton University’s WordNet. Full sources and licences.