Mentioning Christianity would have been redundant since the nation was already an exclusively Christian nation. The founders did not, however, want to create an exclusively Baptist nation, or an exclusively Methodist nation, etc..
For example, Oliver Ellsworth, a Connecticut delegate to the Constitutional Convention of 1787, in explaining to the people the clause that prohibits a religious test for public office, stated, "A test in favor of any one denomination of Christians would be to the last degree absurd in the United States. If it were in favor of Congregationalists, Presbyterians, Episcopalians, Baptists, or Quakers, it would incapacitate more than three-fourths of the American citizens for any public office and thus degrade them from the rank of freemen."
On swearing to a belief in God at the time of appointment or admission to government office, Ellsworth resolved, "His (an officeholder) making a declaration of such a belief is no security at all. For suppose him to be an unprincipled man who believes neither the Word nor the being of God, and be governed merely by selfish motives; how easy is it for him to dissemble! How easy is it for him to make public declaration of his belief in the creed which the law prescribes and excuse himself by calling it a mere formality."
Ellsworth summarized by arguing that it must be left to the people to ensure the people elected and appointed to public office be of high moral character and not selfishly motivated, rather than via some legislated formality. We, the People, are ultimately responsible for moral leadership.
It is clear the Founding Fathers favored traditional Christian moralities; but they were also concerned with government legislated ideologies of a selective, immoral or oppressive nature. However, they were just as fearful of government legislating religious morality out of our lives.
For example, in his Farewell Address, George Washington warned we should forever be "indignantly frowning upon the first dawning of every attempt to alienate any portion of our country from the rest or to enfeeble the sacred ties which now link together the various parts." He added, "With slight shades of differences, you have the same religion, manners, habits, and political principles. You have in a common cause fought and triumphed together."
On the instructions of George Washington I wear an indignant frown, and I wear it like crown.
There were a number of Jews in the American colonies, several of them prominent in the Revolution, including Haym Salomon, the "financier" of the patriot cause, Isaac Franks, aide-de-camp to General George Washington, and Francis Salvador, the first identified Jew to be elected to an American colonial legislature, the only Jew to serve in a revolutionary colonial congress and the first Jew to die for the cause of American liberty. There may have even been a few Musslemen, from the Muslim parts of the British Empire, Hindus too I suppose, but neither would have had the numbers of the Jews.
That's not to say there were as many Jews proportionally as today, but then again there weren't as many Catholics either, even not including the Hispanic catholics of today, since that was also before the large waves of legal immigration of Irish and Italians.
Agreed, on the above statement.
Mentioning Christianity would have been redundant since the nation was already an exclusively Christian nation.
So, imagine that you, as (presumably) a Christian, were helping to form a new nation for Christians (including all the denominations) specifically... Wouldn't you say so somewhere in the most important legal document of that country? Just a word about it. Yet, they covered every other detail and left that out.
That's why this subject is so open to debate and will always be so. Even the wording of the Declaration of Independence gives them the appearance of Deists, with terms like "the Laws of Nature" and "Nature's God" and "Creator". There's nothing very specifically Christian in that document, either.
The other writings of the different men can be presented and examined, but their coming together to create those very important documents speaks volumes. It seems that they were more concerned with the principles of natural law than with the more specific tenets of Christianity... which may be exactly what you were saying... hehe... and I'm the one being redundant now...?