That Bradford game was an embarrassment, no doubt about it, but it was very close to kicking off between Blues on the lower tier behind the goal because of that chant. From memory only the stewards/cops removing a couple of the ringleaders cooled it down. Generally though, I don't recall any concerted racist chants from City fans home or away during the 70s and 80s when it was widespread elsewhere. You'd hear the odd individual comment but despite the leafletting the NF didn't get that much of a hold at City in those days.
I've been going since 1968 and hardly remember any racist incidents except the odd shout or comment from individuals. There was one big fat obnoxious bloke who sat in the south stand and everytime a black player was injured used to shout, "Throw a burning tyre on him." He got a fair few looks and the odd comment and just kind of disappeared, I presume he got banned.