I believe that the limit is based on the person. Many people are different and no two people are the same. For instance someone may be okay if a joke is made about their ethnicity where another person can take that as very offensive. However, people usually take offense to ethnicity, sexism, and family/things that are close to them.
I think the limit is how much they single out a certain race. If they offend all races equally, I don't think they are technically offending anyone.
It becomes offensive when it's offending. If you speak about comedy, then it's just the comedian's job, though.