Specifically?
Well, probably, nothing, as such conduct would have been unthinkable. (Homosexuality openly flaunted, in particular.)
Most restaurants don't place signs saying, "Please don't spit on our floor," but that doesn't mean they think it is okay.
Washington did say, however:
"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...We ought to be no less persuaded that the smiles of Heaven can never be expected on a nation that disregards the eternal rules of order and right which Heaven itself has ordained."
--George Washington Inaugural Speech to Congress April 30, 1789
Anyone who (like Washington) believes the Bible, knows that "the eternal rules of order and right which Heaven itself has ordained" includes prohibitions against homosexuality.
I don't believe the Founders were perfect -- nor did they expect perfection in others. However, a blatant FLOUTING of biblical standards would have been frowned upon, for it is to say that the Bible is wrong, God is wrong, and that homosexuality is normal. It is not, and I believe the laws of the colonies at the time of our country's founding likely reflected such a view.
That would have pleased a majority of the major names. Adams might be an exception, although he was also a rather catholic Christian. Try again.