For starters it wasn’t exactly “private” as the letter was published in a Massachusetts newspaper a month after Jefferson had written it. As for the main aspect, while technically, it is correct in that the phrase, ‘wall of separation between Church & State’ does not appear in the U.S. Constitution, it was Jefferson’s interpretation of the First Amendment.
Such various writings of the Founding Fathers, besides the U.S. Constitution, are important because they provide an insight into how they thought about the issues. So these writings are important in how we go about interpreting particular points of the Constitution. If they thought this way in public (or even private) writings, this is how they were likely to think when they went about framing the Constitution. So the Danbury Baptist Letter is useful in that regard.
One problem with the provided link is the claim, “So, does a private letter constitute enough clout to set a standard in our Supreme Court, when there is NOTHING else to back it up?” That is simply wrong. There are many other pieces of writing to back it up. Some other writings by some of the Founding Fathers on this subject prove this:
“I have examined all the known superstitions of the word, and I do not find in...[the] superstition of Christianity one redeeming feature. They are all alike founded on fables and mythology.”
--Thomas Jefferson, author of the Declaration of Independence and 3rd President of the United States
“Christianity neither is, nor ever was a part of the common law.”
--Thomas Jefferson
“The day will come when the mystical generation of Jesus, by the Supreme Being as his father, in the womb of a virgin, will be classed with the fable of the generation of Minerva in the brain of Jupiter.”
--Thomas Jefferson
“...an amendment [to the Virginia Bill Establishing Religious Freedom] was proposed...inserting the words, ‘Jesus Christ...the holy author of our religion,’ which was rejected By a great majority in proof that they meant to comprehend, within the mantle of its protection, the Jew and the Gentile, the Christian and the Mohammedan, the Hindoo and the Infidel of every denomination.’”
--Thomas Jefferson in his autobiography
“This would be the best of all possible worlds, if there were no religion in it!”
--John Adams, 2nd President of the United States
“...the government of the United States of America is not in any sense founded on the Christian Religion.”
--Treaty of Peace and Friendship, ratified by the Senate during Adams’ presidency
“Who does not see that the same authority which can establish Christianity in exclusion of all other religions may establish, with the same ease, any particular sect of Christians in exclusion of all other sects? That the same authority which can force a citizen to contribute threepence only of his property for the support of any one establishment may force him to conform to any other establishment in all cases whatsoever?”
--James Madison, Father of the Constitution
“Congress should not establish a religion and enforce the legal observation of it by law, nor compel men to worship God in any manner contrary to their conscience, or that one sect might obtain a pre-eminence, or two combined together, and establish a religion to which they would compel others to conform.”
--James Madison in his 1789 Annals of Congress
“...no religious test shall ever be required as a qualification to any office or public trust under the United States.”
--Article VI U.S. Constitution