That is a load of star-spangled bull feathers. The very preamble of the Declaration of Independence is a complete refutation of the Calvinist doctrine of election. Calvinism does not teach that "all men are created equal, that they are endowed by their Creator with unalienable rights". They believe that a very special few are selected before the dawn of time to special and spiritually superior.
Calvinism doesn’t deny the Preamble.
In fact, Calvinism affirms the Preamble.
All men are indeed created equal — equally fallen and equally in need of God’s grace. And the Creator has endowed all men with the right of life (who else gives life), liberty (who else gives liberty) and the pursuit of happiness (we each seek happiness according to our inclinations.)