Even if all 56 members of the 1787 U.S. Constitutional Convention were Deists and none were Christians, one must still judge the Constitution strictly by its own content, apart from its authors' alleged Deism. Great cognitive dissonance may exist between artists and their art. That was absolutely the case in this instance.
Deists were optimistic on human nature, i.e., man is born good or can self-perfect. Deists were also Unitarians. Unitarianism subordinates individuality to unity (e.g., Voltaire's "enlightened despotism," or Rousseau's "general will"). In crafting the U.S. Constitution, the Founding Fathers rejected both those Deistic credos.
Instead they hewed to a script perfect for Puritan Whigs. They freely admitted to Whiggery in the British constitutional tradition. Both the U.S. Bill of Rights and Declaration of Independence stressed historic rights of Englishmen against rulers. "Natural rights" meant these restraints on otherwise-tyrannical civil government:
Taxation by consent of property owners; trial by jury of peers; presumption of innocence; due process of law before property seizure; liability for unlawful property seizure; speedy trial; no standing army in peacetime without consent; no quartering of troops in private homes in peacetime without consent; freedom of travel in peacetime; regular legislative sessions; free legislative debate; the right of the general militia (not just of the select militia) to bear arms; habeas corpus; no excessive bail or fines; no cruel or unusual punishments; the right to petition; free elections; and no martial law in peacetime
The Founding Fathers may not have seen themselves as political Puritans. Yet they functionally and effectively were. These 18 rights of Englishmen scream pessimism on human nature
. They shout that rulers threaten human liberty. This was very un-Deistic but most Calvinistic (as in old-fashioned total human depravity).
They were also Trinitarian, not Unitarian, in their constitutional application of the principle of shared sovereignty in federalism, separation of powers, and checks and balances. Trinitarianism, unlike Unitarianism, subordinates neither individuality (3 Persons) nor unity (one God) to the other at the divine level.
Political Trinitarianism shares sovereignty between individuality (many states) and unity (one federal government) at the human level. Sovereignty is logically indivisible. It is an all-or-none concept. "Shared sovereignty" is oxymoronic, like being half-pregnant. Nevertheless the Constitution does divide sovereignty.
The Constitution's silence on secession proves its Trinitarian shared sovereignty. Had it allowed secession, states would be ultimately sovereign. Had it nixed it, the federal government would be ultimately sovereign. Pessimism on human nature, and Trinitarian shared sovereignty, may not Christianize their proponents. But they do "non-Deist-ify" the Constitution. Deism is as Deism does, and there Deism did nothing. Guessing at men's internal religious states is folly. (Even angels cannot tell "wheat" from "tares" – Matthew 13: 24-29.) Pragmatically and objectively, their U.S. Constitutional artwork was profoundly anti-Deistic.