You must have the Republicans confused with the Libertarians.
From a secular-humanist point of view, there is no particular reason to ban public nudity. But the government was intended to reflect the morals of the people. Where does it say in the Constitution that the people of this land should be secular-humanists?
Geo. Washington in his farewell address said this form of government will not work unless people are moral. "[A]nd let us with caution indulge the supposition that morality can be maintained without religion". 1796
History shows time and again God calling people unto Himself, and people falling away and 'doing their own thing'. "There is a way that seems right to a man, but in the end it leads to death." Prov. 14:12