Sen. Tim Kaine is wrong. The idea that human rights are "God-given" is at the foundation of universal human rights applicable to everyone, everywhere. If the rights are "gifts" of politicians and governments, they can be taken away by the whims of those in power, such as Trump.
Of course, Kaine's concerns about theocracy (such as Iran) are correct. But the founders of the United States did not imply that rights came from the human institutions of religion (something they also opposed). They meant that every person has natural, inalienable rights.