If we are going to get technical then we did rebel against religious authority. You cannot separate (at least back then) the crown from the Church of England.
I would highly recommend reviewing again the Declaration of Independence and the preceding peaceful appeals from the colonies to resolve her issues with the crown.
Which the response was to send the king's navy and army across a huge ocean. Now the Christian thing to do would be to not put those American subjects under military occupation. But, no George III had to get back those hicks and their wilds waaaay over that big ocean. Not one drop of blood would be shed if George just kept his troops home and did not engage in military adventurism.
Now on a serious note. Given 17th and 18th century modes of travel and communication, ruling and governing from thousands of miles away across a big ocean is not efficient government. It is not responsive to the people. Frankly impractical. That led to local government becoming independent of the slow course of decisions from central government.
So from a practical and efficient stand point the DoI was right on. George III and Parliament blew it. They could have had a peaceful resolution and the American colonies still loosely affiliated with the crown. Instead they sent troops. Then those troops came to specifically grab the guns of the local militia and therefore you have the 2nd Amendment.
The affiliation with the English Crown did not even really need to be that loose. The actual constitutional issue, in the British sense, of the American Revolution was this:
Each colony had its own elected legislature, and had a tradition of that dating back to settlement. So, the legislatures of each colony were all a hundred or more years old, 160 years old in Virginia's case. There was a long, thick, established tradition in the Americas of local lawmaking and local rule. Common Law of English speaking people (not "The Common Law of England" - the distinction is very important) was applied by elected judges and courts in America for a century and a half before independence. The colonies had charters, which established, after a fashion, a chief executive in the form of a Royal Governor, but within the English system, the governor, as representative of the crown, had the same basic authority as the Crown vis-a-vis Parliament. That evolved in Britain during the colonial period, and it evolved in America too.
The colonists did not start out hostile to the King. The problem was that Parliament, the ENGLISH Parliament, started passing laws after the French and Indian War, that imposed direct taxes on the American colonists. There were always trade restrictions, which came out of Parliament, but historically they had not been enforced. Starting in the 1760s, they started to be really enforced (England needed money for war debt).
The Americans objected to these taxes because they were not represented in Parliament, and "taxation without representation is tyranny". We all know that. What is generally not understood is that the American colonists argument did not end there. The colonists did not argue that they should be represented in Parliament. Not at all. In fact, they argued that the colonies were much too far away to be ABLE to represented in Parliament.
Rather, the colonists argued that each colonial legislature WAS ITSELF a Parliament. So, the American argument was, in essence, that the King was the monarch over a SERIES of Parliaments, each supreme within its own realm - the British Parliament in Great Britain, the Virginia Parliament in Virginia.
The English Parliament was acceded certain privileges regarding the monarchy itself, BUT the English Parliament was NOT competent to legislate for the Americas. The colonial Parliaments were each the legislature for their colonies, with the King as monarch.
This was the 17th Century concept of parliamentary supremacy applied in the colonies, at the time of their founding and forward. It confronted the philosophy of Parliamentary supremacy over the Empire, which developed in the 18th Century in England but not in America. King George had a choice. In essence, he could choose to be King of the British Empire, with its supreme legislature being THE Parliament of London, or he could be King of the United Kingdom with its Parliament, and King of Virginia with its House of Burgesses, and King of Massachusetts with its General Assembly, and King of New York with its Assembly, etc.
English constitutionalists of the time of the American Revolution sided firmly with the constitutional view of Parliament as supreme, not just over the monarch, but over all OTHER English-speaking "parliaments", but the view of Lord Coke a century earlier, in the English Civil War period, was the view of the American colonists.
BOTH sides actually had a constitutional view rooted in British tradition. The American view - their their legisatures WERE their Parliaments, with the King as monarch, was the view of Lord Coke and the 17th Century. The view of Parliament in London as THE Parliament, supreme legislature of the empire, and supreme over the monarch, was the view of England in the 18th Century.
In the English Civil War, the concept of Parliamentary supremacy over the Crown was established (and confirmed in the Glorious Revolution of 1688), and in the American Revolution, the concept of national parliaments in faraway colonies being "Parliament" for constitutional purposes was established for the Americans (America was, for all practical purposes, the "British Empire" of that period - it was only after losing America that the British went out and captured the familiar 19th Century British Empire.
Who was right? Well, they both were right according to their principles. In such things, might makes right, and the Americans won. So that settled it, for America. Canada followed the other model: Dominion. Local legislative rule, distant monarch with local Royal Governor. Essentially, from the American experience the British realized that they could not hold onto English speaking European colonies abroad with a concept of British Parliamentary superiority. When Canada and Australia, New Zealand and South Africa (and later the other countries) became sufficiently developed, their own parliaments became sovereign and the authority of the British Parliament ended, but the Crown remained.
It's a pity that the Americans and British couldn't come to that circumstance peacefully in the 1770s, because the world would have been very different indeed, and probably better, had the English-speaking peoples remained united.
Men become stupid and violent over theories of political power, however. The "Dominion of America" would have been great.