How offensive is the word “cunt” in Australia?

Just to round off what others have said: yes, it is mostly a more vulgar counterpart of the Australian term bastard, and it almost always refers to men rather than women. (The reductionist misogynist use of cunt to refer to women is unknown here. I only discovered it a few years ago)

Just like bastard, if it is qualified by an adjective, it is typically informal, jocular, or dismissive, rather than outright offensive, in “lower” social contexts. (Australia does have classes, but it also has a lot of mobility between class registers: the new money millionaire can float between low and high class discourse. Old Money doesn’t, but Old Money isn’t as prominent as it used to be.)

Used on its own, though, it is still vicious. When someone called me a cunt because my dog crapped on his nature strip? He was getting ready to punch me, the roid rage rising to his head, the fists clenching; and cunt was the most hostile term he could spit out at me.

And you do have to judge your registers for appropriateness. There is a jocular, low register with ribbing and swearing and no actual harm done. But that’s not 24/7, even for the so-called lower socioeconomics.