> White is a cultural definition in the US which used to be legally defined and still carries cultural implications.
I guess where some non-Americans feel concerned about this, is the tendency to export US discourses about race to the rest of the English-speaking world (and even the world more broadly), despite the fact that other countries have different histories and cultures and understanding of what the words mean.
The Australian Human Rights Commission recommends analysing racial and cultural diversity in Australia in terms of four broad categories [1] – Indigenous, Anglo-Celtic, European, and non-European. ("European" is defined to exclude Anglo-Celtic people.) Slightly reminiscent of the American "one drop rule", people of mixed backgrounds are assigned to the more diverse background. By contrast, the US has an official classification of people into five different races [2].
Australia does have a rather horrible history of racial discrimination – for example, the "White Australia Policy" which for decades banned non-European immigration. However, I think the way Australian officialdom (governments, academics, etc) have tried to deal with that, is to avoid using racial categories like "white", and focus primarily on culture and multiculturalism. They are happy to talk about different ancestries/nationalities/cultures (Italian, Chinese, Indian, Lebanese, etc), but grouping them into racial categories is avoided in official contexts, although it still sometimes happens in less formal contexts. (Journalists sometimes talk about "Asian Australians" or "African Australians", but the government prefers to talk about Chinese and Filipinos and Sudanese and Eritreans.) When it is necessary, they'll split them into not explicitly racial groupings like Indigenous/Anglo-Celtic/European/non-European. That splits two groups of people both considered "white" in the US (Anglo-Celtic and European), while lumping together as non-European both some people officially considered "white" in the US (e.g. Lebanese people), and also multiple non-"white" races (Asian, African, Pacific Islander).
I think Australia's ways of dealing with its history are at times quite different from those of Americans, precisely because their histories are in many ways quite different. But I think many Americans unconsciously assume that understandings of race and culture that make sense in a US context must make sense for the rest of the world as well.
[1] https://humanrights.gov.au/sites/default/files/document/publ...
[2] https://www.census.gov/topics/population/race/about.html
(Throwaway because I'm scared of talking about race and culture using my real name.)