Do South Park episodes mean to offend people in a joking way or an actual mean way?

Both. The show is happy to offend people who are actually offended because they take the subject matter way too seriously.

Those of us who can laugh are allowed to laugh and not be offended.

It's all how you take it.

IMO..... they do not give a rat's donkey who they offend.. they just want to be as gross as they can get-away with....some of what they comment on is some bad stuff that needs to be put down... corrupt political stuff and just the general crap people get involved with.... but the way they go about it is most often just as disgusting as what they are "satirizing"

Yes