Dear Fester,

You are absolutely right: Hatred is our enemy, not people.

"Every vicious thought will rebound, every thought of hatred which you have thought, in a cave even, is stored up, and will one day come back to you with tremendous power in the form of some misery here. If you project hatred and jealousy, they will rebound on you with compound interest. No power can avert them; when once you have put them in motion you will have to bear them. Remembering this will prevent you from doing wicked things." - Swami Vivekananda

Metaphysically speaking, every tragedy is entirely self inflicted, whether or not we can see the links.
No, it would not be appropriate to feel empathy with "neo Nazis in Romper Stomper", yet it is appropriate to feel compassion for them once they suffer the inevitable retribution. Compassion for the people, not empathy with their hatred.