The First Amendment has to be read in 18th C. language. The classical interpretation is narrow: that the federal government is prohibited from establishing a national religion like the Church of England. Establishment of a religion was reserved to the several states and to the people. Only quite recently, in the 20th C. liberal era, has legal opinion broadened to interpret the clause as prohibiting any federal spending for religious purposes. That view is liberalism, not constitutionalism.
The Bill of Rights dealt very specifically with limitations on federal powers. The First Amendment is not to be read without reference to the Tenth, which reserved powers prohibited to the federal government to the several states and to the people. The states did exercise that power. Massachusetts, Connecticut, New Hampshire, Georgia and Maryland all passed taxes specifically to support the Christian religion. Individuals generally were given the right to earmark their taxes to the church of their choice.
Article VI, stating that "no religious Test shall ever be required as Qualification" for federal office holders, is about all the Constitution had to say about religion.
My quote shows it to apply to 'ANY office'. You simply deny the wording?
The Bill of Rights dealt very specifically with limitations on federal powers.
Your contention is unsupported by the actual language of any of the first ten amendments, nor the preamble. In fact the Preamble makes clear the BOR's are to be considered "as part of the said Constitution. --"