If you think that Trump and the Republicans are all about honoring the Constitution as it was written, you're mistaken. According to the Republican Platform:
"The Declaration sets forth the fundamental precepts of American government: That God bestows certain inalienable rights on every individual, thus producing human equality; that government exists first and foremost to protect those inalienable rights; that man-made law must be consistent with God-given, natural rights; and that if God-given, natural, inalienable rights come in conflict with government, court, or human-granted rights, God-given, natural, inalienable rights always prevail; that there is a moral law recognized as “the Laws of Nature and of Nature’s God”; and that American government is to operate with the consent of the governed."
So to summarize: whatever rights the Republican Party thinks are innate under the god of their choosing supersede the document they claim to revere.
First, there are two clarifications which must be made:
1. There is only one use of the word “God” in the combined entirety of the Declaration of Independence and Constitution, which is the “Nature's God” quoted in the Republican Platform above. Note that this is not just any god. It is not even a religious god. It is the God of Nature. This does not correspond with the Republican Party's assumption of the Christian God.
2. The exact wording is of the Declaration of Independence's statement on unalienable rights is: "We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights." Is the wording meant to say that all people have the same creator, that there is only one Creator? I would argue that, had that been the intention, they would have said "endowed by the Creator". My interpretation of the wording allows individuals to acknowledge their own creators.
One may argue that it is unlikely that the founding fathers had that interpretation in mind; however, I would rebut that if the argument is that the founding fathers were infallible, then we must accept what they wrote and what they did not write. The possessive before "Creator" is, to my mind, the critical word. “A Creator”, “the Creator”, and “their Creator” all have different meanings. Whether intentional or not, the founding fathers chose the word that allows the greatest personal variation of who or what that Creator is.
Regardless, the point must be made that at no point did the founding fathers specifically credit the Christian God with the origin of our unalienable rights. As any writer can tell you, specificity is the soul of narrative.
Moving on from the Republican Platform's lack of internal validity, we have another issue. If MY God and MY God-given rights are different from the Republican Party's, then the Republican Party infringes on my first amendment right to freedom of religion (which, to be clear, means that I have both the freedom to practice the religion of my choice, and the freedom to not have other religious beliefs or practices imposed upon me).
The only rights the founding fathers felt compelled to spell out in the Declaration of Independence as unalienable are Life, Liberty, and the pursuit of Happiness. And to be clear, these rights are not god-given, they are "endowed by their Creator."
Given the existence of slavery and inability of women to vote at the time of our nation's birth, obviously the founding fathers didn't really mean that all people have unalienable rights to Life, Liberty, and the pursuit of Happiness.
I see three options:
1. We accept the Republican Party's infringement on our constitutionally protected rights.
2. We accept the Constitution as it was intended by the founding fathers. We revoke the equal rights amendments added later because if the founding fathers wanted women and Blacks to have rights, they would have said so.
3. We accept the spirit of the Constitution (that it is a document designed to protect all citizens' rights, not revoke them) and make legislative, judicial, and executive decisions accordingly.