The primary duties of the Monarchy are those set out in the Coronation Oath. In that oath, a new King or Queen pledges to:
to govern the Peoples of the United Kingdom of Great Britain and the Dominions, and the Possessions and the other Territories to any of them belonging or pertaining, according to their respective laws and customs.
to do all in their power to cause Law and Justice, in Mercy, to be executed in all decisions.
and
to the utmost of their power maintain the Laws of God and the true profession of the Gospel? To maintain in the United Kingdom the Protestant Reformed Religion established by law? Tom maintain and preserve inviolably the settlement of the Church of England, and the doctrine, worship, discipline, and government thereof, as by law established in England? And to preserve unto the Bishops and Clergy of England, and to the Churches there committed to their charge, all such rights and privileges, as by law do or shall appertain to them or any of them.
The third part of this oath is the part that makes the Monrarch Fidei Defensor - Defender of the Faith. And it most directly refers to their duty to uphold the established Church of England and its doctrines, not Christianity in general.
The Monarch's duties (and those of their Heirs and Successors according to law) goes further than just the Coronation Oath, however. It's governed by Constitutional Convention, and except in emergency situations (such as a collapse of Parliamentary government) the duties are subject to very strict control. The Monarch cannot express public views that are at odds to those of their government and Prime Minister unless the government and Prime Minister are acting outside convention themselves. The Prince of Wales speech in Copenhagen was probably written by somebody at the Foreign Office to present Her Majesty's Governments position, and if it wasn't written there, it was certainly cleared there.
The modern Monarch functionally has three roles and rights - to advise, to be consulted, and to warn. If the Monarch disagrees with his or her government, he or she can say so in private. There are other powers, some of them significant, but most of these only come into play if particular circumstances apply, and none of them are relevant here.
Her Majesty's Government has the constitutional right to both negotiate an agreement, to sign that agreement, and attempt to persuade other nations to do, if it chooses to do so. It's not exceeding the authority of Parliament. And so the Monarch's hands are tied.
The only potentially relevant power that applies in this case is one of the Lascelles Principles, which gives the Monarch to power to take certain steps in a case where the national economy is under serious threat. But even if that was considered to be relevant, all the Monarch could do is dissolve Parliament and call an election - something that has to happen by next June anyway.
Where exactly during the course of history did the Monarchy gets its authority? Few people on this earth will ever sit on that continuous promised earthly throne. And during the course of history there have been some Godly ones and then others that turned their back on Him.
It is beyond ridiculous to be claiming that man made climate change is going to cause starvation and terrorism. Most especially when it literally means that US are going to be the ones to fill up this new age collection plate. And more so it is against Christ.... and the Ten Commandments, and the promise made long ago to Noah after the flood. Genesis 8:21 And the LORD smelled a sweet savour; and the LORD said in His heart, "I will not again curse the ground any more for man's sake; for the imagination of man's heart is evil from his youth neither will I again smith any more every thing living, as I have done.
22 While the earth remaineth, seedtime and harvest, and cold and heat, and summer and winter, and day and night shall not cease,"