Edit: I didn't mean to imply that it's not a problem now - but it's no means as big a problem as it used to be (and I have direct experience through family members of horrific bigotry towards and to Catholics in Scotland).
Funny thing about the "people still get knifed at Old Firm games" comment itself is that it raises something that isn't really a problem so much anymore (Rangers/Celtic hadn't met in four years until September, where there was one arrest out of ~60,000 fans) and misses the stuff that really is an issue - areas which are still deeply segregated + gang violence split along these lines, provocative/offensive songs, flags and banners used by both sides at the football
But as you said - it's nothing like what our grandparents' generation would have experienced, or what went on in Northern Ireland during the Troubles.
I remember having a rather surreal experience a few years back, sitting at a bar on the Meadows during the festival with the Lady Boys of Bangkok on one side and an Orange Walk on the other.
I'd have said it went all the way back to the Civil War and the Jacobite insurgencies. Certainly NI's sectarianism is explicit about the Battle of the Boyne 1688.