Invoking a deity in your deceleration of independence doesn't mean you are creating a country based on religion. "Nature's God" is a Deist idea, written by a Deist. Also, Deism rejects revealed religions (e.g., Catholicism, Baptists, etc...)
I think the problem is that people read the Declaration and assume we're founding a country. No. The Declaration says, " Screw you George, we're breaking up with you and here are the reasons why." It severed the ties between England and the Colonies. It did not establish a separate government. We were not founded to be a Christian nation. We are a nation that allows you to practice what you want (a concept lost on all those that protest and disturb other religious observances.)
So break it down for the dummies. We can all agree that:
The Declaration of Independence - List of grievances to justify secession from England
The Constitution of the US - Document that establishes the gov't of the United States with no references to God.
- Spoiler: show
We the people of the United States, in order to form a more perfect union, establish justice, insure domestic tranquility, provide for the common defense, promote the general welfare, and secure the blessings of liberty to ourselves and our posterity, do ordain and establish this Constitution for the United States of America. God isn't in the Preamble to the Constitution nor is it anywhere in the document.
Also, I guess we should consider the Treaty of Tripoli, ratified by the US Senate and signed by John Adams, he himself a founder of the country:
As the Government of the United States of America is not, in any sense, founded on the Christian religion; as it has in itself no character of enmity against the laws, religion, or tranquility, of Mussulmen [Muslims]; and as the said States never entered into any war or act of hostility against any Mahometan [Mohammedan] nation, it is declared by the parties that no pretext arising from religious opinions shall ever produce an interruption of the harmony existing between the two countries
Gotta make those Arabs happy, right. Damn Barbary pirates!
One historian has noted, pertaining to Article 11:
By their actions, the Founding Fathers made clear that their primary concern was religious freedom, not the advancement of a state religion. Individuals, not the government, would define religious faith and practice in the United States. Thus the Founders ensured that in no official sense would America be a Christian Republic. Ten years after the Constitutional Convention ended its work, the country assured the world that the United States was a secular state, and that its negotiations would adhere to the rule of law, not the dictates of the Christian faith. The assurances were contained in the Treaty of Tripoli of 1797 and were intended to allay the fears of the Muslim state by insisting that religion would not govern how the treaty was interpreted and enforced. John Adams and the Senate made clear that the pact was between two sovereign states, not between two religious powers.
~ Frank Lambert in his book,
The Founding Fathers and the Place of Religion in America. It's a good book.