i think theres two camps of offensive humour. theres humour which is good but also offensive, and then theres 'humour' which consists solely of offence - the punchline is child sex abuse or the n word, and the only reason anyone laughs is shock (or theyre just... awful).
for a mild version, think "whats red and goes round and round?" "a baby in a blender." its not very clever, the setup and payoff that makes comedy work is weak, and it really relies entirely on shock factor. better examples of poor offensive humour lie in joke sites for things like madeline mckan (i know this bc i spent a year around a guy whose entire sense of humour relied on offence)
OH also a great example is basically all of james gunn's early work and the tweets that got him #cancelled - it was just child abuse and statements about child abuse with no craft around them at all, just the idea that the shock should be funny.
so yeah, while i can certainly take issue with well crafted offensive humour (depending on the situation and what we define as offensive), i can also enjoy it if its good - but most offensive humour is just shit