How does Family Guy get away with the stuff they do?

Answer 1

That's a rather broad question but basically it's freedom of speech.

FOX allows them to make the jokes they do because people watch and FOX makes money from the show.

There's still censorship going on, after all, "Partial Terms of Endearment", the episode that deals with Lois Wrestling with the decision whether or not to have an abortion or not has been banned in the U.S.

Also, "Get away with" implies that there is something wrong with what they do. They are just as entitled to say what they like as anybody else is; the difference being they have an established and relatively popular company to assist them in saying it loudly.

Answer 2

Assuming you mean making fun of them.... it's called parody. Parody is protected under the law.

Also, by the mere fact they have chosen to be in the public eye, they automatically (perhaps unfortunately in some cases) open themselves up to ridicule and satire.