Ashkenazi Jews, and some Sephardi were ok under White Australia, no restrictions. In fact one of them was probably the empire's best WWI general.
Monash's parents migrated from Germany to the colony of Victoria in the 1850s, before there was a Commonwealth of Australia or immigration restrictions
of any form, let alone the WAP. The White Australia Policy heavily restricted immigration from anywhere other than the British Isles, including European countries. For a clear idea of how the White Australia Policy restricted Jewish immigration, you have to look at the years
when it existed, and critically, those years when the most Jews were seeking to emigrate from Europe; in July 1938, at the Evian Conference, organised to find destinations for the Jews desperate to escape Austria, Germany and Poland, the Australian delegates' statement was that "
we have no real racial problem and we are not desirous of importing one." Australia accepted
no Jewish refugees following the conference.