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In this case, I'm amazed saying "Australia is a republic" isn't being counted as simple vandalism. Repeatedly putting in misleading and plainly factually incorrect information certainly counted as vandalism when User:Michael was going hogwild at it.
Well, perhaps because you need to do more than point out the ceremonial role of the monarch to make your case, that appears to be all those with some aversion to a straight forward application of the word "republic" have done.
I suspect there is something we are missing to this controversy, perhaps the words "republic" and "constitutional monarchy", have been hijacked as labels for political constituencies in those countries, much like "life" and "choice" in the USA. If, the controversy is real, then it should be noted, although not necessarily in the introduction. But the other side should get their say.
This ususually works out, although sometimes some weasal words are also needed in the intro. This is what makes wikipedia more useful than "respected" encyclopedias, even the intro might give you a clue that the establishment status quo is being questioned.
-- Silverback