Then let's re-phrase the question. If what you say is true, and the authors of the Constitution actually wanted a federal government based in religion, why didn't they write that into the Constitution?
The expectation was that only religious people could be elected, as shown by the discussions around the "religious test" phrase.
The only "religious test" allowed would be that the person taking the oath of office believes in a Supreme Being, and in a future state of
rewards and punishments, since that was the legal requirements needed to take the oath at the time the Constitution was written.
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James Iredell in the North Carolina Ratification Convention (Hillsborough), Wednesday, 30 July 1788
. . .
But it is objected that the people of America may, perhaps, choose representatives who have
no religion at all, and that pagans and Mahometans may be admitted into offices. But how is it
possible to exclude any set of men, without taking away that principle of religious freedom
which we ourselves so warmly contend for? This is the foundation on which persecution has
been raised in every part of the world. The people in power were always right, and every body
else wrong. If you admit the least difference, the door to persecution is opened. Nor would it
answer the purpose, for the worst part of the excluded sects would comply with the test, and
the best men only be kept out of our counsels. But it is never to be supposed that the people of
America will trust their dearest rights to persons who have no religion at all, or a religion
materially different from their own.
. . .
According to the modern definition of an oath, it is considered a "solemn appeal to the
Supreme Being, for the truth of what is said, by a person who believes in the existence of
Supreme Being and in a future state of rewards and punishments, according to that form which
will bind his conscience most."
. . .
Ever since this great
case, it has been universally considered that, in administering an oath, it is only necessary to
inquire if the person who is to take it, believes in a Supreme Being, and in a future state of
rewards and punishments. If he does, the oath is to be administered according to that form
which it is supposed will bind his conscience most. It is, however, necessary that such a belief
should be entertained, because otherwise there would be nothing to bind his conscience that
could be relied on; since there are many cases where the terror of punishment in this world for
perjury could not be dreaded. I have endeavored to satisfy the committee. We may, I think,
very safely leave religion to itself; and as to the form of the oath, I think this may well be
trusted to the general government, to be applied on the principles I have mentioned.
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And why would they specifically prohibit religious tests for public office?
You probably didn't read this the first time I posted it.
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Theophilus Parsons in the Massachusetts Ratification Convention Debates, 23 January 1788
…It has been objected, that the Constitution provides no religious test by oath, and we may
have in power unprincipled men, atheists and pagans. No man can wish more ardently than I
do, that all our publick offices may be filled by men who fear God and hate wickedness; but it
must remain with the electors to give the government this security—an oath will not do it: Will
an unprincipled man be entangled by an oath? Will an atheist or a pagan dread the vengeance
of the christian’s God, a being in his opinion the creature of fancy and credulity? It is a solecism
in expression. No man is so illiberal as to wish the confining places of honour or profit to any
one sect of christians: But what security is it to government, that every publick officer shall
swear that he is a christian? For what will then be called Christianity? One man will declare that
the christian religion is only an illumination of natural religion, and that he is a christian;
another christian will assert, that all men must be happy hereafter in spite of themselves; a
third christian reverses the image, and declares, that let a man do all he can, he will certainly be
punished in another world; and a fourth will tell us, that if a man use any force for the common
defence, he violates every principle of Christianity. Sir, the only evidence we can have of the
sincerity and excellency of a man’s religion, is a good life—and I trust that such evidence will be
required of every candidate by every elector. That man who acts an honest part to his
neighbour, will most probably conduct honourably towards the publick.
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