Not sure what you mean by "institutionally scared of non white immigrants". In 2014/15 the vast majority of immigrants were from Asia: https://www.border.gov.au/ReportsandPublications/Documents/s...
Nevertheless, within the institutions of politics and media and to a lesser extent the civil service there remains a vocal and sizeable minority who fear white people and "anglo-white" culture will become the minority and become oppressed.
Fortunately, most Australians don't feel that way.