I'm Australian, born in the 1980s, spent my whole life here. I can tell you growing up we rarely (if ever) thought about "who is what race". In part it is a cultural thing – in my lifetime, official Australian society (government/media/etc) has discouraged talk of "races", encouraging people to instead identify via finer-grained nationality/ethnicity/culture labels – i.e. "Chinese" or "Indian" or "Vietnamese" not "Asian", "Irish" or "Italian" or "Polish" not "white", etc. The whole "who is what race" thing sounds very American to my ears. I believe that way of thinking is becoming more common here, as Australia becomes more Americanised through social media and other sources, but I'm not inclined to see that as a positive development.
That's not to say there is no problem with racism in contemporary Australia. I remember at my high school, there was a significant minority of students of Lebanese ancestry (it was a Catholic high school, so our ethnically Lebanese students were predominantly Maronite Catholics) – and I definitely remember hearing some mildly prejudiced things said about them, even to their faces. But, in all that, I doubt anybody was ever asking themselves "are Lebanese people white?"
One of my school friends, who is of partial Italian descent (albeit via Argentina/Uruguay rather than directly), had to put up with dumb jokes at school about his dad being in the Mafia. He told me how when his father first moved to Australia in the 1970s, his coworkers would exploit his poor knowledge of English to trick him into saying offensive things to the boss. What "race" are my friend and his dad? The question seems pointless, irrelevant. At least here in Australia, "racism" is generally defined as prejudice on the basis of "race, colour, descent or national or ethnic origin" – so it isn't necessary to categorise a person as belonging to any particular "race" to acknowledge them as a victim of racism.
How then does one describe this difference between the US and Australia – between a society which strongly (and maybe even increasingly strongly) focuses on coarse-grained racial categories, and a society which (in recent decades) has had a strong tendency towards avoiding them? Maybe "racial blindness" isn't quite the right term for it, but it seems at least somewhat adjacent.