That's to be regretted, because it means Australia continues to be headed by monarchs who inherit the throne according to laws which should have no place in a modern nation (even if we do manage to accommodate the idea of an inherited monarchy).
Succession to the English throne is still governed largely by the Act of Settlement of 1701, which specifically excludes not only Roman Catholics, but anyone who marries a Catholic. The monarch must be Protestant, and become part of the Church of England communion.
In addition, the monarch carries the title Defender of the Faith, and is automatically Supreme Governor of the Church of England. This may be appropriate for England, if you accept the idea of an establishment church.
In Australia, our founding fathers were determined not to import sectarian nastiness from the old world, and wrote this into the Constitution:
The Commonwealth shall not make any law for establishing any religion, or for imposing any religious observance, or for prohibiting the free exercise of any religion, and no religious test shall be required as a qualification for any office or public trust under the Commonwealth.
No religious test required – except, that is, to inherit the position of King or Queen of Australia.
In another provision which should be anathema in a modern nation, the Act of 1701 bases succession on the rules of male primogeniture. A woman cannot inherit the throne if she has a younger male sibling. (In Britain, this is unlikely to be a practical issue for many years, if ever – but it's still a relic of times when women had inferior status.)
Over recent years in Britain, there have been moves to change these rules but nothing much has happened.
Contrary to monarchists' claims today, a decade ago most Australians did support a republic – but a majority of them wanted nothing short of a republic in which the public elected the president. They declined to vote for the “minimal change” model put to them in the referendum, under which the president would have been elected by a two-thirds majority in a joint sitting of the Federal parliament.
For the then Prime Minister, John Howard – a committed monarchist – it must remain a proud achievement. As Grumpy Old Journo wrote in this post in February last year, Howard used a brilliant “wedge” strategy to halt what appeared to be Australia's inexorable loosening of ties with the “mother country”.
First, he set up a Constitutional Convention which argued for a couple of weeks before agreeing on the “minimal change” model which was put to the electorate. With a small majority, it supported a parliamentary vote to select the President, rather than a national election, because it would not disrupt constitutional arrangements which were working well. And that's where we lost.
Tony Abbott and other Liberal leaders said the position of President would be far too important to be decided by politicians. We should vote no to a republic so we didn't have the President elected by politicians.
It worked. It seemed Australians didn't know that under the existing, continuing arrangement, one person – the Prime Minister, possibly but not necessarily in consultation with a few cronies – chooses the Governor-General. The British monarch must accept the Australian Prime Minister's nomination.
Howard was also able to exploit two weaknesses in the republican cause. As historian Stuart Macintyre wrote in the second edition of his Concise History of Australia:
The first was the very celebrity of the republicans. [Malcolm] Turnbull's movement used prominent writers and artists, recruited television personalities, business and sportspeople. Their enthusiastic advocacy could be dismissed as an example of the estrangement of the elites from the practical concerns of the battlers.
The second weakness was to campaign for the minimal republic.
Their chief argument turned out to be no more than an appeal to national prejudice: Australia should not have a foreigner as its head of state. Since an Australian governor-general already exercised the functions of the head of state, this allowed monarchists to divert the republican debate into an arcane argument over constitutional law.
It also did not help the republicans that Howard also drafted a new preamble to the Constitution, and put it to the electors in the same referendum. The electors duly rejected both questions. As Macintyre wrote:
. . . he produced a preamble of startling banality that invoked mateship, refused to recognise Aborigines' prior occupancy of the land, and took a gratuitous swipe at political correctness.