Both the adopted statement and Jefferson's original statement (which is closer to the statement contained in George Mason's Declaration of Rights which Jefferson likely used as a template:
Virginia Declaration of Rights - Wikipedia, the free encyclopedia) are statements encapsulating the believe in "Natural Law" a concept which considered certain rights to be ordained and granted by the Creator. To assert that Jefferson meant anything other than that certain "natural" rights were divinely granted is to warp the historical context in which his statements (original and adopted) were written.
Natural law - Wikipedia, the free encyclopedia (my emphasis).
And, just so we're clear as to Jefferson's beliefs in drafting the Declaration:
"Well aware that the opinions and belief of men depend not on their own will, but follow involuntarily the evidence proposed to their minds; that Almighty God hath created the mind free, and manifested his supreme will that free it shall remain by making it altogether insusceptible of restraint; that all attempts to influence it by temporal punishments, or burthens, or by civil incapacitations, tend only to beget habits of hypocrisy and meanness, and are a departure from the plan of the holy author of our religion . . . ."
-- "A Bill for Establishing Religious Freedom," Section I
"For in a warm climate, no man will labour for himself who can make another labour for him. This is so true, that of the proprietors of slaves a very small proportion indeed are ever seen to labor. And can the liberties of a nation be thought secure when we have removed their only firm basis,
a conviction in the minds of the people that these liberties are the gift of God? That they are not to be violated but with his wrath? Indeed I tremble for my country when I reflect that God is just: that his justice cannot sleep for ever . . . ."
-- "Notes on the State of Virginia" (my emphasis)
Both quotes
Jefferson -- Quotations on the Jefferson Memorial
As 24 of the 56 signers of the Declaration of Independence held seminary degrees, I would suggest that, rather than "pandering to religion", the Declaration's language reflects the deeply held beliefs of the signers that the natural rights of man were, in fact, a gift of God.
Founding Fathers Quotes - Christian Quotes of the Founding Fathers
You may disagree with their beliefs and conclusions but to assert that they did not hold them is simply wrong.