sympathy has 2 distinct synonyms spread across 2 of its 3 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
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.
an inclination to support or be loyal to or to agree with an opinion
“his sympathies were always with the underdog”
sharing the feelings of others (especially feelings of sorrow or anguish)
Synonyms, antonyms and the broader and narrower relations for sympathy come from Princeton University’s WordNet. Full sources and licences.
a relation of affinity or harmony between people; whatever affects one correspondingly affects the other
“the two of them were in close sympathy”