I think it's both, it's not just an empathy thing because they do have empathy: but only for their family, their neighbors of colors, etc. It's more selective sure, but it's still empathy.
I've seen conservatives say they feel (have empathy) for the women in Jacob Blake's life, and the children, but not for Jacob himself. Or at least not since he became an adult and chose to perpetuate the cycle.
I think it's more complex than that all (or even most) republicans are racist.