Anything that's so hateful or disgusting that you can't bear to think about it is detestable. Many little kids find all green vegetables to be utterly detestable.
It's pretty common for people to find hate speech detestable, as well as stepping on slugs in bare feet and the pungent smell of garbage. The verb detest means "hate" or "strongly dislike," and the adjective detestable brings in an element of disgust or offensiveness. The Latin root, detestabilis, means "abominable," from detestari, "curse or express abhorrence for."