Yep, most rivalries in sport are simply based on the sport itself or local derbies or differing social classes etc... but Celtic and Rangers goes way beyond all of that. They have been a factor in civil wars and everything. It's an almost inhuman intensity they have towards other at times.
It's mostly sectarian and violence is a common consequence when their fans clash on the streets. I myself have seen a guy get absolutely brutalized in Northern Ireland for simply wearing Rangers shorts. 3 (presumably) Celtic fans just battered him relentlessly until they were physically restrained... it is frightening.