I'm not going to get into the issue of the exact etymology of 'Judeo-Christian', suffice to say its current popularity is a post-WW2 phenomenon. It's very unlikely that many members of the Commonwealth parliament or bureaucracy were familiar with this concept in 1901.
Also, yeah, our settler-derived society was institutionally racist against, as OPer notes, anyone from Western and Northern Europe,
for multiple reasons stemming from the grim complexity of 19th century nation building. See Western Canada and the United States for pretty much the same thing.
It's important to note that the drafters of that document were all clamouring to claim the edge in our particular liberal consensus, hence the above clause. It passed with almost no dissent, IIRC.
Perhaps more importantly, the power to deal with immigrants on the basis of their 'racial alien' status also passed easily,
https://en.wikipedia.org/wiki/Section_51(xxvi)_of_the_Constitution_of_Australia