Back in the 1960s and 70s, jokes about mother-in-laws, Blacks, Irish, Italians and Pakistanis were rife in Britain, especially in comedy and working men's clubs in the north. It's only recently, since the early 1980s, that this type of humour has been condemned as being racist and sexist. Jewish jokes in the UK were generally taboo, but if you watch a few Dean Martin YouTube videos, you'll catch a few Jewish jokes, mainly told by Don Rickles and Sammy Davis Junior—both Jews.
One day on a golf course with Jack Benny, he [Davis Jr.] was asked what his handicap was. "Handicap?" he asked. "Talk about handicap. I'm a one-eyed Negro Jew."
Some jokes were always in poor taste, but there were a few that were not meant to offend but were simply taking the mickey.
British TV shows like Benny Hill Show, Rising Damp, Are You Being Served?, Love Thy Neighbour and the Canadian show, Bizarre, were all hugely popular in their heyday but would now cause a storm of outraged tweets on Twitter.
Jokes at the expense of women were not called sexist but: blue, dirty, adult humour, or, more vulgarly, piss taking.
Jokes about the Irish and their infamous stupidity were called Irish jokes, and if I remember correctly, jokes were always classified this way; blue jokes, Irish jokes, Paki jokes, etc.
One British comedian, Bernard Manning, (in)famous for telling ethnic and minority jokes, said to his detractors: "I tell jokes. You never take a joke seriously."
Wikipedia recounts an episode, which illustrates how his style of humour was eventually viewed as racist.
In 1994, two black waitresses at a charity dinner at a hotel in Derbyshire took exception to Manning's act and appealed to an industrial tribunal against the management of the hotel for racial discrimination. They lost, later to have the decision overturned at appeal, where they won an undisclosed sum. Manning felt that the word "wog" was "a horrible, insulting word I've never used in my life" but defended use of the words "nigger" and "coon" as historical terms with legitimate roots.
When the northern comedian died in 2007, The Daily Telgraph added this timely observation
Many feared (or quietly rejoiced) that a whole genre of comedy, an entire species of comic, had died with Manning. Had the forces of political correctness and modish "alternative" comedy killed them off?
Note, the journalist never categorises Manning's comedic style as being blue or off-colour, which in British English could be anything between saucy (titillating) and pornographic.
Today, ironically, if an American-born comedian told racist, ableist, homophobic or sexist jokes in public or on TV, they'd be crucified, but they might be elected as the president of the USA.