Unless he's an avowed Satan worshiper I have no issues with how he worships the God upon which the Constitution was based.
Let's leave aside for a moment that the Constitution was in no way whatsoever based on Christianity, the Bible, Protestantism, or G-d. We could discuss it, but the evidence on one side is tediously complete. The stuff on the other is wishful thinking and (not to put too fine a point on it) lies told by people who want their religion to rule rather than law and democratic institutions.
Take a look at the Constitution itself. It states (Article VI) that "no religious test shall be used for any position of public trust". That isn't an ammendment. It's one of the foundations of the original document. What I'm worried about when the President-elect raises his right hand is that he will "
will faithfully execute the office of President of the United States, and will to the best of my ability, preserve, protect and defend the Constitution of the United States" to quote directly. Personal spiritual beliefs mean nothing, less than nothing compared to his or her determination to carry out that solemn Oath.
In fact, excessive piety may disqualify a person for the office. Someone who places religious convictions above the law or says that a "higher imperative" supersedes the legal responsibilities of the office is unfit for the job and has sworn an oath falsely. If he or she hands over any portion of the decision making to an external religious authority be it the Pope, an Ayatollah, James Dobson, the LDS Council of Apostles or the Dalai Lama that person is forsworn. One of the most enraging things I ever heard from the Supreme Court was Clarence "Uncle" Thomas saying that the Bible was his supreme authority when deciding legal matters. His only authorities can be the written law and legal precedent with the Constitution trumping them all. Anything else is a violation of the office.
Jimmy Carter is certainly a committed Christian. I disagree with many of his religious beliefs, but he never let them come between himself and the duties of the office as he saw them. George W. Bush claims to be a committed Christian. He holds the Constitution in utter contempt calling it "that damned piece of paper" and using his office to make his religious beliefs (or those of his Masters in the Reconstructionist/Dominionist Right) supplant the law. In both cases the character of the two men is what is important. The particular sect or cult to which they belong is at best secondary.
John Kennedy ran into Protestant anti-Catholicism. The real issues were American Protestant distrust of the Roman Church and a better founded worry that he would bow to ecclesiastical pressure when making exercising his powers of office. It seems that those fears were unfounded. If Mitt Romney can stop flip-flopping, waffling and repositioning long enough for us to figure out exactly what he believes - other than that he believes he wants to be President - it would make some sense to examine his record and see how much if at all he will defer to the LDS Church in matters of policy. The same can be said of the various evangelical Protestant groups and megachurches and the more conventionally Protestant candidates.
Frankly, the only one who doesn't bother me is Obama. He's had some Muslim education. And no, the Republican Lie Machine is true to form; it wasn't at an Islamist madrassa. He is a Christian. In other words he's read more than one book and has a tad more objectivity than most of the candidates when it comes to religion. Joe Lieberman is an Orthodox Jew. I'm a Jew. It wouldn't make me any more likely to vote for the opportunistic lying son of a *****.