I don't mind offensive humour in general, because humour is an excellent way to process things.
However, there are variations of offensiveness.
Simply kicking down at marginalized groups, or making light of victims' experiences generally are the bad type of offensive, and it comes to no surprise much of it are in poor taste. Making fun of rape victims, or victims of genocide, grieving families, that kind of thing. That stuff is not okay imo, because it's done at the expense of someone who already has gone through unspeakable suffering, they don't need you to point your finger at them and laugh at their pain, loss or death.
If you want to have good offensive humour, make fun of the perpetrators. Those are the ones deserving of being ridiculed, of being ravaged by sarcasm.