The quality of being repugnant: offensiveness, repulsion.
The quality of being repugnant: (logical) opposition, contradiction, incompatibility.
1710, George Berkeley, A Treatise Concerning the Principles of Human Knowledge, Part I, Dublin: Jeremy Pepyat, pp. 175-176,
[…] this Notion is the Source from whence do spring, all those Amusing Geometrical Paradoxes, which have such a direct Repugnancy to the plain, common Sense of Mankind, and are admitted with so much Reluctance, into a Mind not yet debauched by Learning […]