I want to know the answer to the following question:
What did this menace undermine?
All the background I'm provided with is that "After the First World War, however, it became apparent that the number of mixed-race people was growing at a faster rate than the white population, and by 1930 fear of the "half-caste menace" undermining the White Australia ideal from within was being taken as a serious concern.". Is that enough to answer the question?
Answer: yes