Yes and no. Sure, 'hate' is probably the wrong word, and may be counter productive in many cases. And you're right about the empathy; everyone likes to apply labels that mean they don't have to feel.

On the other hand, accusing the people you oppose of being demonic Satan-spawn looking to corrupt our youth and destroy our lives and country, of being the baby-molesting other that causes nightmares, well, that probably isn't caused by an excess of good feeling.