Take their (Mormon) polytheism for example: as oddly fascinating and even appalling a doctrine as it is, you have to get behind it to understand its implications. Behind it is something called "the eternal progression": the god who created this world — the God of the Bible, they claim — was once a man living on a planet created by his father god, who was once a man living on his planet created by his father god and so forth. Now there is a philosophical problem with this: there is no beginning point — it is an infinite regress. But there can not be such a thing, because if you have to go back an infinite number of times, you never get to a beginning and without a point at which to begin, you never get to now and today. That is an insurmountable philosophical (logical) problem.
But more pertinent to the political question is the moral problem it generates. According to Mormon doctrine, the way that each god gets to become a god is by following the "law of the gospel." To Mormons, law (not god, or God) is eternal and law is prior (although "prior" has no real meaning when one is talking about an infinite regress) to god (or to God). God has not created law, it is not "of Him" or "from Him," rather, "law" — impersonal and uncreated -- has made the gods gods (made Him God).
This is not merely a radical departure from the Judeo-Christian concept of God, it is a radical deformation of the concept of law, both natural law and the positive (promulgated) laws that flow from it:
The natural law, the Creator's very good work, provides the solid foundation on which man can build the structure of moral rules to guide his choices. It also provides the indispensable moral foundation for building the human community. Finally, it provides the necessary basis for the civil law with which it is connected, whether by a reflection that draws conclusions from its principles, or by additions of a positive and juridical nature (CCC 1959).
Behind the Declaration of Independence and the Constitution stands precisely this Judeo-Christian concept of natural law as the participation of the human conscience in the eternal law of God. It is eternal because it "is the work of divine Wisdom" (CCC 1950), and has as its source an eternal Being, God. It is this concept of natural law from which positive law (ecclesiastical and civil) derives its just authority and its appeal to human reason. Furthermore it is exactly this concept of law that allows us to insist that no law can ever make abortion or euthanasia or embryonic stem cell research lawful.