I think you are taking an outcome and confusing it with a value. I notably don't like right wingers, but even I don't think they love to hate. I think left and right leaning people have different deeply held values and seeing someone who appears to not care about those values stand in your way of achieving them can be very upsetting.

I value community and having right wingers openly say that if a child's family cannot feed them that's not their problem upsets me. I'm sure right wingers value autonomy and personal responsibility and a lot of other things that make my insistence on child food programs upsetting to them. Neither side wants to hate inherently, they just want opposing things and the other side is literally stopping them.