The President plays a lot more roles than to merely set policy. He is a role model for the nation. That’s why I would never vote for a Mormon, even if I agreed with their policies because it would be promoting a false religion.
Warren Jeffs did exactly the same thing that Joseph Smith did. And for that matter that Mohammed did. They all proclaimed to be prophets, they all claimed that prior scripture had errors and omissions. And that allowed them to overturn scripture and introduce their own social policies, so that they could create their own personal sex and power fest.
Mormonism has partially refined itself. It’s rejected the “eternal covenant” of polygamy. It has made small modifications in the objectionable parts of it’s scripture so many times that the current Mormon scriptures barely resemble the originals. And I hear they no longer dwell on many of the most objectionable teachings. So they have moved somewhat towards mainstream Christianity. But they still teach much error.
You still fail to explain how electing a person for a secular office is in any way “promoting” the religion of that elected official.