I think there's actually a huge difference between being a British Subject and being an Australian Citizen, and obviously so too does the High Court of Australia, for in very recent times it has ruled quite a number of those elected to the 45th Parliament of the Commonwealth of Australia as ineligible based on the federal Constitution's Section 44 i
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Section 44 of the Constitution sets out restrictions on who can be a candidate for Federal parliament. Simply put, the following cannot be eligible to be a Member of the House of Representatives or the Senate ... The Section in part reads:
44. Any person who -
(i.) Is under any acknowledgement of allegiance, obedience, or adherence to a foreign power, or is a subject or a citizen or entitled to the rights or privileges of a subject or citizen of a foreign power:
So prior to the Australia Act of 1986, those with UK or NZ dual citizenship status, were NOT in breach of that section (the UK was not yet a foreign power!) but AFTER 1986, that's when the UK became a foreign power in respect of Australia.
If you were to write 'I guess there is not that much difference because once you were a naturalised British Subject, you could then qualify for pension, vote and get an Australian issued British Passport' ...... but until 1949, there was NO such status as Naturalised Australian. You wrote about your Swedish ancestor being granted Australian citizenship in the early 1900s... That is simply not possible. Foreigners were those who were NOT British Subjects either by birth or naturalisation.
JM