There's an impact at the region level. Sympathy for a realm you're at hatred with will drop dramatically in your regions, making it ultimately more difficult for your opponent to hold onto your regions if they conquer them. It can slow them down.
Or is there? I haven't observed this, despite the flavor text. We kept getting messages about locals being unhappy with the war with Sint. Seemed more like fluff text than anything.
Also, when I ceased the hatred, it had a message about morale loss among the soldiers. I did not notice drops in region stats.
