I don't see a lot of point to having a ceremonial head of state thousands of miles away, but if the Aussies and Kiwis want to claim King Charles III, feel free. Your call -- and in the modern world, it's up to the voters no matter what the theory may say.
Unlike the Stuarts the monarchs who rule us are bound by a Protestant constitution and their powers are limited to such a degree that you barely notice they are there except in a ceremonial capacity. But while it is a Protestant constitution I will claim him as my king for good or ill. It's not really a call to make. It just is. And like the rest of life you take the good with the bad thankful to Providence for the daily benefits that He loads upon us.
Fair point -- you are obligated by the Word of God to pray for kings and all that are in authority, as I am obligated to pray for President Biden for the next few weeks until his term of office ends -- but some qualifications apply.
As you know, many and perhaps most of the British colonies have long ago cut their ties with the Monarchy and more may do so in the future. We no longer live in a world where divine right of kings applies and in which John Calvin was quite concerned, in his correspondence with John Knox, not to appear (at least in writing) to give support to Knox's views that a crowned head of state could be removed by lesser magistrates for gross idolatry, apostasy, or other extreme sins. In the context of the 1500s and 1600s, Knox's views were not just radical but revolutionary, and would have been interpreted by rulers all over Europe as "proof" that Calvinists were closet Anabaptists of the Munster stripe, seeking to overthrow all authority and order, and should therefore be regarded as not only ecclesiastical heretics but political traitors.
Now things would be different if you were a Christian living under an absolute monarchy, and they'd probably be different if you were a Christian living someplace like Thailand with a monarch who is mostly ceremonial but where the laws on "lese-majesty" (defamation of the sovereign in his person or his office) are not mere formalities but are taken quite seriously and actually enforced.
But you are not. Furthermore, you are thousands of miles away from England and Scotland and have your own governing body separate from the British Parliament to conduct your own affairs.
Perhaps the closest Reformation-era parallel I can think of would be some of the semi-independent city-states near the borders of medieval Switzerland whose city councils had an ancient right to select a new sovereign ruler upon the death of their previous sovereign, and usually preferred to select a sovereign far away who would have little actual say in the day-to-day affairs of the city-state. Some of those city-states eventually ended up become Swiss cantons.
We both concur that the political problems of Australia and New Zealand are far worse than the faith of your crowned head of state, or lack thereof. There really isn't much point in asking your members of parliament to introduce legislation to amend your relationship with the monarchy. It's a ceremonial role and little else.
But while you as an individual subject of the crown don't have any more ability to say "King Charles is not my monarch" than I have the ability to say "Biden is not my president" (and yes, I did choose that example deliberately because some American conservatives **DO** say precisely that, and are violating Scripture as well as facts when they say such things), you as Australians or New Zealanders do, not individually but corporately, have the legal right to break ties with the Crown, as many other British colonies have done.
So I should have been clearer in what I said. No, you (individually speaking), as Matt Winzer, do not have the call to make on whether King Charles is or is not your monarch. As you correctly say, "It just is."
But you (speaking as a plural), do have the right acting corporately through your elected representatives to do so.
That's what I meant to say when, speaking more casually and flippantly that I should have done, I wrote this: "...if the Aussies and Kiwis want to claim King Charles III, feel free. Your call -- and in the modern world, it's up to the voters no matter what the theory may say."
This is mostly theory, of course. Removing the monarchy and becoming a republic would not help either of your two "down under" nations or their religious problems. On the contrary, it is my understanding that "republicanism" in Britian is associated with left-wing politics and I would guess the same applies "down under."