The Declaration of Independence is not United States law. It has substantial moral weight in our country, but zero legal weight.
The Supreme Court has ruled multiple times that the First Amendment requires the separation of church and state. See Everson v. Board of Education and Engel v. Vitale. Supreme Court rulings are considered United States law.
In addition to the First Amendment, there is Article VI, Section 3 of the Constitution, which reads "no religious test shall ever be required as a qualification to any office or public trust under the United States." So technically any oath of public office that forces a person to state they believe in God is unconstitutional. "So help me God" is not offically in the Presidential oath of office - it has just become a tradition.
Think about it this way - if religion is allowed to influence politics, then politics has to be allowed to influence religion. Do you really want politicians in Washington determining what the preacher at your local church can or can't say?
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