"Separation of Church and State" never appears in the Constitution but rather in the dicta of a Supreme Court Decision.

That being said, the so-called doctrine of "Separation of Church and State" does not mean that the President (or any other government official) cannot be a religious person or make religious references in speeches or statements.

Here is the text of the First Amendment:

Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof

The first part is generally referred to as the "Establishment Clause" and merely states that the government cannot establish a "government religion". The second part is generally referred to as the "Free Exercise" clause and allows for everyone (even the President of the United States) to freely practice and believe in any religion he or she chooses.

The phrase "Separation of Church and State" was contained in a Supreme Court decision and it was even commented on by a Justice that it was likely a poor choice of words and that it would be misunderstood. Today if you asked 1000 people where that phrase was found 999 of them would say with conviction that it is found in our Constitution. Today this phraase is being used as a tool to remove all aspects of religion from our government, schools, and any other public area. You may recall the recent attacks on our Pledge of Allegiance, the removal of the Ten Comandments in many courthouses, and now a renewed attack on the phrase "In God We Trust" printed on all of our money.

There is no difference between these attacks to remove ALL religion or reference to God and the establishment of a government sanctioned religion. The interpretation of "Separation of Church and State" has become so mired in politics and misunderstanding that the actual words of the Constitution have been forgotten.

Go read the Constitution and you will be surprised at what you will find.