Mmmmm, I'm not sure it wasn't always there. My Grandad (RIP) recalled times when colleagues nearly came to blows at work over football - working with Cidereds and Sagheads was no different even back in the '40s (he was from Cardiff, BTW!)
As others have said, I think trouble existed, but it wasn't as organised or as widely publicised. The 1970s was when it all really kicked off.
My personal recollection is of games in the '80s, Millwall at home in c.'85??? We lost 1-0 and it literally turned into a riot, police dogs, horses, the lot, fans in the Dolman ripping up seats and throwing them at the Millwall fans. I was in the old enclosure and utterly terrified (I was 15). City had a pretty poor reputation back then, probably deservedly so. Our record on racism towards players was nothing to be proud of, either.