If you have very negative, even hostile feelings about something, you're antipathetic toward it. If you're antipathetic to a particular basketball team, you'll root enthusiastically for whatever team they're playing against.
The adjective antipathetic and noun antipathy come from the Greek antipathes, "an opposition of feeling," and its roots anti, "opposite," and pathein, "to suffer or feel." It's not quite full-on hatred, but an antipathetic feeling is a strong aversion or distaste. If your cousins are antipathetic to furry animals, you might want to reconsider inviting them to stay for two weeks — they won't enjoy hanging out with your four cats, three dogs, and affectionate chinchilla.