If you've not been paying attention for the past 200 years or so, the executive has tremendous influence over the values and morality that are perpetuated by legislation and executive decision during their term of office. Through influence on Congress and the selection of SCOTUS candidates, the sexual, religious ... whatever preference of the President comes into play on shaping our nation's community values.
You may claim to be above it, but however you reached your beliefs, they are still, in fact, your beliefs, and you cannot operate otherwise. So you may claim that your beliefs were developed in a secular vacum carefully avoiding any hint of religious overtone. That means you will naturally be out of step with 90% of Americans who when recently polled identified themselves as being influenced by faith in God. It comes out in decisions like, what should our response be for Haiti? How important is abortion funding in HC legislation? What is a just war?
If the President comes from the middle of the pack in those formative influences that shape his morality, then pluralism and freedom have a strong chance of surviving. If however they come from the edges of the community, right or left, then pluralism suffers, and freedom becomes marginalized. I find it difficult to imagine that a true Muslim, or lesbian wiccan, could serve in the office of President and not feel the pull to promote and further their worldview in some manner small or large.