Thank you Emma for this great question. To become a member of the Australian Parliament a person must be at least 18 years old, an elector able to vote for the House of Representatives and an Australian citizen. In the past Aboriginal and Torres Strait Island peoples and people of non-European backgrounds have not had these rights.
The Commonwealth Electoral Act 1902 excluded all ‘aboriginal native[s] of Australia, Africa, Asia or the Islands of the Pacific except New Zealand’ from voting unless they could vote in state elections. In most states, Aboriginal and Torres Strait Islanders peoples were ineligible to vote. From 1920 all migrant British subjects except Pacific Islanders were able to vote in Australian elections. (In 1925 this was extended to non-British Indians). However, the Immigration Restriction Act 1901 had stopped non-white immigration to Australia, and Pacific Island and other non-white migrants had been deported.
Aboriginal and Torres Strait Islander peoples were granted Australian citizenship along with all other Australians in 1948. (Before this all Australians were British subjects). Citizenship did not give voting rights to Aboriginal and Torres Strait Islander peoples though. This was guaranteed by the Commonwealth Electoral Act 1962. The first Aboriginal member of parliament was Senator Neville Bonner in 1971.
Non-Europeans were not given a path to citizenship by the Nationality and Citizenship Act 1948. This did not happen until 1957 but only after a person had been a resident for 15 years. This requirement was lowered to 3 years (the same as for British migrants) in 1973. The first Asian-Australian member of Parliament was Tsebin Tchen who entered the Senate in 1999.