Religion in the Declaration

There are four references to God in the Declaration:
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The "laws of nature and of nature's God" entitle the United States to independence;
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Men are "endowed by their Creator with certain unalienable rights";
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Congress appeals "to the Supreme Judge of the world for the rectitude of our intentions";
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The signers, "with a firm reliance on the protection of divine Providence," pledge to each other their lives, fortunes, and sacred honor.
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Were these explicit references to religion — specifically, Protestantism?
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The very short answer: Possibly, but not exactly.
Religion in the Americas, 1700s

The story of religion in America’s original 13 colonies often focuses on Puritans, Quakers and other Protestants fleeing persecution in Europe, looking to build a community of like-minded believers.
Protestants were indeed in the majority, but the reality was far more diverse. Colonial America attracted true believers from a wide array of backgrounds and beliefs, include Judaism, Catholicism and more. Not to mention, the indigenous peoples and enslaved Africans also had their own beliefs and practices.
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It is true that most of the Thirteen Colonies were founded as distinct Protestant societies, with their own charters and, with a few exceptions, an emphasis on religious uniformity. Exceptions to this rule include Rhode Island and Maryland.
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That said, on the eve of the American Revolution, no single Protestant denomination could claim more than one-fifth of the colonies’ religious adherents. Meanwhile, many of the Founding Fathers were followers of Deism, a set of Enlightenment ideas vaguely grounded in opposition to religious orthodoxies that were marked by skepticism, rationalism and the close observation of nature. (Some Deists, such as Thomas Paine, rejected Christianity outright.)
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The founding documents of the Revolutionary period — including the Declaration of Independence — recalibrated the role of religion away from government.
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(This section is summarized from this article.)
Why was God referenced in the Declaration?
To be sure, the words could be referencing the Judeo-Christian God. However, and critically, it needn’t be seen as limited to a specifically Christian, or even Judeo-Christian God, but (unsurprisingly) it seems to be tracking at least two of that god’s major attributes.
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This is especially worth keeping in mind because Jefferson, the main writer of the document, was one of the more religion-skeptical leaders of that era. Basically, Jefferson was a firm theist, but not necessarily of the traditional Christian divinity.
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In 1825, Jefferson described the purpose of the Declaration like this (emphasis added):
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“This was the object of the Declaration of Independence. Not to find out new principles, or new arguments, never before thought of, not merely to say things which had never been said before; but to place before mankind the common sense of the subject, in terms so plain and firm as to command their assent…it was intended to be an expression of the American mind, and to give to that expression the proper tone and spirit called for by the occasion. All its authority rests then on the harmonizing sentiments of the day.”
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​The Declaration of Independence was a reflection that the American natural rights republic was rooted in the natural law. The natural law described the rights given to human beings by reason and by God. But the Declaration isn't specific on whose God, only acknowledging the existence of a God. It broadly appeals to people's sense of reason by using rhetoric that would have been familiar to readers of the time.
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In other words, comments with literal religious significance from this time period must be understood in the context of social convention as much as theology. For example, one might tell a bereaved spouse that they could look forward to meeting again in the afterlife — in the 1700s, this wouldn't only be taken literally, it would also be commonly understood as a way of expressing empathy.
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If nothing else, Jefferson's inclusion of those phrases indicates just how pervasive religious language was in governmental documents of the time — and how legitimate such language was seen as being. The Framing generation was certainly quite comfortable with not just religious but even theological rhetoric in government speech.