"No people can be bound to acknowledge and adore the Invisible Hand which conducts the affairs of men more than those of the United States. Every step by which they have advanced to the character of an independent nation seems to have been distinguished by some token of providential agency; and in the important revolution just accomplished in the system of their united government the tranquil deliberations and voluntary consent of so many distinct communities from which the event has resulted can not be compared with the means by which most governments have been established without some return of pious gratitude, along with an humble anticipation of the future blessings which the past seem to presage. These reflections, arising out of the present crisis, have forced themselves too strongly on my mind to be suppressed. You will join with me, I trust, in thinking that there are none under the influence of which the proceedings of a new and free government can more auspiciously commence."
Washington, one of history's greatest leaders, chose his words carefully to unite people of various faiths and denominations. I don't believe this was an attempt to push moral or religious relativism, however. Very few of the Founders would've embraced postmodern relativistic nonsense that says one religion is "true for you," while another is "true for me." (Either God is real or God is not. Either Jesus really rose from the dead or he did not. Either Mohammed was a prophet who spoke for Allah - or he was not. While people have many opinions about religion, opinions don't determine ultimate reality). Washington's speech doesn't advocate relativism. Rather, it expands the tent to include many faiths. This was, I believe, the hope of many Founders who saw the violence that unchecked sectarianism could bring in other nations, such as in post-Reformation Europe. Obviously, truth claims would continue in the churches, synagogues, and mosques (and there is nothing wrong with this....truth claims should be tested and evaluated in the marketplace - including the religious marketplace - like all else) and no faith or denomination would be asked to compromise their beliefs or convictions. But Washington's monotheistic call for national homage to God was such that most Americans (be they Muslims, Jews, Baptist, Methodist, Anglican, etc.) could embrace with a clear conscience.
While there may be debate over which Founders were orthodox Christians (and which were not) or whether the Founders intended some kind of official "Christian nationalism" (as claimed by some activists), the evidence is overwhelming that George Washington's sentiments, as expressed in his First Inaugural (and later his famous Thanksgiving Proclamation and Farewell Address), reflected the overwhelming consensus of the American people at the time as well as the principles and ideals which were enshrined into our nation's heritage.