Au contraire...
You have simply adopted a 1962 erroneous attitude.
This is the exact meaning articulated by its own author, James Madison. After reviewing this same historical context of the Establishment Clause, Chief Justice Rehnquist concluded:
It seems indisputable from these glimpses of Madison’s thinking, as reflected by actions on the floor of the House in 1789, that he saw the Amendment as designed to prohibit the establishment of a national religion, and perhaps to prevent discrimination among sects. He did not see it as requiring neutrality on the part of government between religion and irreligion (Wallace v. Jaffree, 1985).
"I have sometimes thought there could not be a stronger testimony in favor of religion or against temporal enjoyments, even the most rational and manly, than for men who occupy the most honorable and gainful departments and [who] are rising in reputation and wealth, publicly to declare their unsatisfactoriness by becoming fervent advocates in the cause of Christ; and I wish you may give in your evidence in this way (“Madison Letter...,” 1773, emp. added)."
The Northwest Ordinance, passed by Congress in 1789, provided that “[r]eligion, morality, and knowledge, being necessary to good government and the happiness of mankind, schools and the means of education shall forever be encouraged” (1789, 1:52).
On the day after the House of Representatives voted to adopt the final version of the First Amendment Establishment Clause, Representative Elias Boudinot proposed a resolution asking the President to issue a Thanksgiving Day Proclamation to “recommend to the people of the United States a day of public thanksgiving and prayer, to be observed by acknowledging with grateful hearts the many and signal favors of Almighty God” (Annals of Congress, 1789, 1:949). This resolution was passed on September 25,
In 1782, the United States Congress passed the following resolution: "The Congress of the United States recommends and approves the Holy Bible for use in all schools."