My mum is Australian (Melbourne) and she says that Australia was certainly very racist when she was there (this was >20 yrs ago).
The "White Australia" policy only ended within her lifetime, and its legacy may be partly to blame as a lot of Australians just didn't have exposure to people of different ethnicities when they were younger, or were led to think of them as inferior/savage.
My mum can remember the first time she ever saw someone with dark skin as event, because there were literally no non-Caucasians growing up. Prior to that she had only seen golliwogs. Yes she had golliwog dolls growing up. All middle aged australians are likely to be in a similar position.
She does however say that there were lots of european immigrants (greeks, italians, germans) whom were relatively well tolerated but generally lived separately to everyone else.
Not all australians are racist (my mum isn't, though she is possibly a little bit more fascinated by race than most people), but racism is a problem still. But improving.