"Swearing-in

The Constitution provides that every Member of the House of Representatives, before taking his or her seat, must make and subscribe an oath or affirmation of allegiance before the Governor-General or some person authorised by the Governor-General.[58] The oath or affirmation takes the following form:

OATH
I, A.B., do swear that I will be faithful and bear true allegiance to Her Majesty Queen Elizabeth the Second, Her heirs and successors according to law. SO HELP ME GOD!
AFFIRMATION
I, A.B., do solemnly and sincerely affirm and declare that I will be faithful and bear true allegiance to Her Majesty Queen Elizabeth the Second, Her heirs and successors according to law.[59]
The oath of allegiance need not necessarily be made on the authorised version of the Bible, although this has been the common practice. A Member may recite the oath while holding another form of Christian holy book, or, in respect of a non–Christian faith, a book or work of such a nature. The essential requirement is that every Member taking an oath should take it in a manner which affects his or her conscience regardless of whether a holy book is used or not."

Can an avowed Republican or an anti-Monarchist, make this assertion of allegiance to the Queen in good faith having declared that they intend to break their allegiance?"

Also moslem members of parliament swear on the Koran.
Catch, isn't there always a catch;
The Koran permits someone to lie, swear an a false oath to an infidel
if it is to the advantage of a moslem.

It is a defense for treason or false swearing.

Most politicians swearing any sort of oath is a joke. They don't even tell the truth very often. And, they are not much different from the people who vote for them

Society has become so fake that truth actually bothers people.

The purpose of an oath or affirmation is not totally useless, at least in theory. In court, for example, one has to give an oath or affirmation to tell the truth, which avoids tiresome denials later if caught in a lie.
Not so sure about oaths and affirmations in Parliament, because politicians can lie often and without consequence.
Part of the problem is mainly discussion about "values" rather than discussion about evidence and logic-based policy.
In theory, we public are supposed to punish the dishonest politicians at the ballot box. The problem is that there are so few "swing voters", so most get away with it.
So lots of baseless claims are made, and many fallacies in logic, and of course no proper evidence or citations of evidence presented.
So the best tactic is to practice critical thinking with no "sacred cows". That means NONE.
We all have some biases, and some of the worst are ones we are not aware of.
And if you ain't a billionaire yourself, why on Earth would you vote for one?

Dear Is Mise,

I think you will find the operative words are 'according to law'.

"Rule According to Law

The rule of law requires the government to exercise its power in accordance with well-established and clearly written rules, regulations, and legal principles. A distinction is sometimes drawn between power, will, and force, on the one hand, and law, on the other. When a government official acts pursuant to an express provision of a written law, he acts within the rule of law. But when a government official acts without the imprimatur of any law, he or she does so by the sheer force of personal will and power."

So those who are observing the law undertake to do so until if and when the law is changed.

Not sure what the issue is.

No person should be in Parliament unless they have fully understood our constitution and with sincere heart intends to follow it. The only way the constitution can be changed is by referendum. Those that intending changing the constitution should not hold office under the constitution.