Why was our nation formed on Orthodox Christian, and not heretical principles? First, Christianity was left to the States to practice as they wished, however, heterodox Christian principles were never a part of the incorporation of legal Christianity, neither in the State or Federal Documents; the heterodox were given freedom of conscience like everyone else, but their minority, at this time, had no inclusion in ANY founding government document.
The various State Constitutions were Orthodox in nature; the heterodox minority in Massachusetts were years away from the Dedham decision of 1820. The majority understood Unitarianism was not part of the Protestant Reformation, having been kicked to the curb by Luther and Calvin, and forever cast out by the Synod of Dort in 1619. Furthermore, the Reformation denounced all forms of Unitarianism, Arianism, and Socinianism, starting with the Gnostics, which were never considered Christian. The majority "Protestant" framers of Massachusetts understood their history. Yes, it's true, a Unitarian wrote most of the 1780 Massachusetts Constitution, however John Adams is only one man, while the ratifiers of that Constitution are most important.
Notice the State Constitution of a Mid-Atlantic State where heterodoxy was a small minority, perhaps non-existent:
Constitution of the State of Maryland (August 14, 1776), stated: Article XXXV That no other test or qualification ought to be required, on admission to any office of trust or profit, than such oath of support and fidelity to this State and such oath of office, as shall be directed by this Convention, or the Legislature of this State, and a declaration of a belief in the Christian religion.” That, as it is the duty of every man to worship God is such a manner as he thinks most acceptable to him; all persons professing the Christian religion, are equally entitled to protection in their religious liberty; wherefore no person ought by any law to be molested… on account of his religious practice; unless, under the color [pretense] of religion, any man shall disturb the good order, peace or safety of the State, or shall infringe the laws of morality… yet the Legislature may, in their discretion, lay a general and equal tax, for the support of the Christian religion (until 1851) [bold face mine].
Not only were the vast majority of Founding Fathers Orthodox, the majority philosophers they studied were as well, including: Arminianist Hugo Grotius, Sir William Blackstone, Richard Hooker, Samuel de Puffendorf, and perhaps John Locke. Yes, Arminius believed in Total Depravity. His only beef with Calvin was free will.
It's true, Locke failed to espouse Church Creeds, or essentials, but so did the Apostles. At Pentecost, there was no Westminster Confession, only faith in Jesus as the Messiah. Clarification of Church Doctrine wasn't made until the 2nd to 3rd Centuries. Notice, Jared Sparks, the former President of Harvard, and his opinion of Locke's faith:
"And Locke must still be considered a Unitarian, till he can be proved a Trinitarian ; a task, which it is not likely you will soon undertake. At all events, he had no faith in the assemblage of articles which you denominate the essence of christianity, and without believing which, you say, no one can be called a Christian. His whole treatise on the Reasonableness of Christianity bears witness to this truth. For the leading object of that work is to show, that "the Gospel was written to induce men into a belief of this proposition, 'that Jesus of Nazareth was the Messiah,' which if they believed, they should have life."* He says nothing about total depravity, the atonement, the "sanctifying spirit of an Almighty Surety," nor any of your peculiar doctrines. Yet who has done more to elucidate the sacred Scriptures, or to prove the consistency and reasonableness of the religion of Jesus? Your rule, however, will take from him the Christian name."[bold face mine]
Sparks shows his understanding of Christian Theology. The Apostles had no assemblage of articles, and "without believing", has nothing to do with salvation, rather, it's the rejection of certain articles the indwelt Holy Spirit cannot affirm.
Did Locke have some unorthodox views regarding the unessential state of nature? Yes. Did he believe in inerrancy? Yes. Did he indirectly defend the Trinity? Yes. Furthermore, Locke could be a heretic, but more serious inquiry is needed to make a clear declaration as to John Locke's faith.