Repugnant expresses a very strong feeling of dislike or disgust, stronger than just 'not liking' something. He had a repugnant taste for food left unattended overnight.
Pro Tip 2/3
Emotional Reaction
Using 'repugnant' suggests a visceral, emotional reaction, not just a rational disagreement. People find cruelty to animals repugnant.
Pro Tip 3/3
Often Moral
Repugnant is frequently used for actions or ideas that people consider morally wrong. Child labor is repugnant to our society's values.