I don't think another rivalry in the country compares in terms of pettiness and just outright hate. They call Georgia-Georgia Tech "Clean old-fashioned hate". State-Ole Miss is just "hate".
Red river shootout is close, but that's it for the US.
When I worked in Argentina, first trip I bought a Boca Juniors shirt, wore it to the plant. Half the guys were grinning and cheering me. The other half glared at me like I just screwed their wife and kicked their dog. Our contact came to me and says "I am keeping half the plant from killing you. When you get to the hotel, change your shirt, pack it and do not wear it again here, it is unsafe".