As @Oddthinking has pointed out, the term "egalitarian" is ill-defined; does egalitarian mean:
- equality of opportunity, or
- equality of outcomes?
Once you have decided on this, do you mean equality in:
- political power,
- social standing,
- body mass index (just kidding)
Your first quote and the first paragraph of the second quote appear to refer to "Australian egalitarianism" as a social construct - an equality of outcome in social interactions i.e. one person is not better than another because of distinctions in birth, wealth or education.
The first article is clear and consistent and is to my mind, as an Australian, what is meant by "Australian egalitarianism". This is and always has been a relative measure - Australian interactions are less formal than European and even American - titles and honorifics (even Mr & Ms) are rare outside of very formal situations and anyone can be addressed as "mate" - regardless of sex, ethnicity or social status. I know this makes my sister-in-law (an Austrian) extremely uncomfortable.
What we are dealing with here is a cultural identity or myth - like all myths it is about how should be - not about how they are or were. Just as Americans want to believe in "the land of the free" and the French in "libertie, egalitie and fraternitie", Australians want to believe that their society is fair and equitable - it isn't, never has been, never will be.
However, the second part refers to an equality of economic opportunity and the article as a whole generally conflates these two very different definitions of egalitarianism.
Equality of economic outcome is easier to measure than equality of economic opportunity so lets get that out of the way first, see
From these, income inequality has increased slightly over the past 40 years by some measures but Australia was about in the middle of the OECD countries then and is still in the middle now. So it has changed but not a lot.
The second article you cite is talking generally about equality of economic opportunity and specifically cites a paper by Dr Leigh which is at best tangential to the anecdotal case the article is about. That paper compares intergenerational income mobility between fathers and sons who were both born in Australia. It is worth quoting the abstract:
Combining four surveys conducted over a forty year period, I calculate intergenerational earnings
elasticities for Australia, using predicted earnings in parents’ occupations as a proxy for actual
parental earnings. In the most recent survey, the elasticity of sons’ wages with respect to fathers’
wages is around 0.2. Comparing this estimate with earlier surveys, I find little evidence that intergenerational
mobility in Australia has significantly risen or fallen over time. Applying the same
methodology to United States data, I find that Australian society exhibits more intergenerational
mobility than the United States. My method appears to slightly overstate the degree of intergenerational
mobility; if the true intergenerational earnings elasticity in the United States is 0.4–0.6
(as recent studies have suggested), then the intergenerational earnings elasticity in Australia is
probably around 0.2–0.3.
What this says is that there is greater intergenerational equality of economic opportunity in Australia than in the US and that this has not changed significantly over time. Put another way, what your father earned has less impact on what you earn in Australia than in the US. This of course cuts both ways - social mobility is not always upwards.
This is then used as a basis for decrying the economic opportunities of a person who is:
- not born in Australia
- has a father who presumably was not born in Australia
- not educated in Australia
- is a relatively recent immigrant
- from an English as a second language country
- working in an unskilled job.
The proposition that because this person does not earn a lot and has little prospect of bettering themselves; therefore Australia is no longer egalitarian is riddled with logical fallacies, both formal and informal.