sensibility has 4 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. Its one recorded opposite is insensibility.
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.
refined sensitivity to pleasurable or painful impressions
“cruelty offended his sensibility”
Synonyms, antonyms and the broader and narrower relations for sensibility come from Princeton University’s WordNet. Full sources and licences.
(physiology) responsiveness to external stimuli; the faculty of sensation
“sensitivity to pain”