It's quite simple, really. Upon winning an election, the to be president has to take an oath "to uphold, protect, and defend the Constitution ..." If, however, people, like Huckabee, declare that the Bible (or Quran, or the Communist Manifesto) should be above the Constitution, then he cannot take that oath without committing perjury. And since the oath is legally binding for as long as he is in power, he also cannot later adopt this position without violating that oath, for then he is committing treason against the country. As either way, he is committing "high crimes and misdemeanors", he is subject to impeachment and prosecution.
This is not a religious test for office. A government official can hold any religious or other ideological ides as he pleases; he just can't, by his actions, impose them against the US and local constitutions. He can even advocate his beliefs, and hold that the Constitution to be amended or rewritten to reflect them; he can't just act on them out of personal conviction or conscience.
Of course, I am alluding to Kim Davis as well, who is basically in the same position. She isn't a county clerk simply she won the largest number of votes; she too must have taken an oath of office which mentioned both the state and federal constitutions. Perjury cannot be proved here, because her views on gay marriage only came out recently. But she is violating her oath by ignoring the Supreme and other courts, those determiners of what constitutions mean. That to is treasonous, albeit on a much smaller scale. It is a crime which should lead to her impeachment and prosecution. And if impeachment is unobtainable, she still should be prosecuted and punished if found guilty. Of course, the honorable thing to do would have been to resign, citing her conscience -- but that wouldn't have brought forth fame, legions of followers/supporters, and guaranteed royalties on the inevitable book (a ghost writer) publishes.
That, ironically, is something she does have the right to do.
