I don't have the original letter that Mason wrote to Livingston; but the context seems he approves of God being invoked in the Articles, but disapproves that the Bible is not referenced as a source of "Supreme Law" for the United States.
And, as we know, the US Constitution didn't even mention God; Mason (and other members of the "religiously correct") flipped out. And 200 years later gave the authors of "The Godless Constitution" fodder for their book.
Livingston's original letter, reproduced below, may be found here.
"TO THE REV. MR. JOHN MASON.
"Princeton, 29th May, 1778.
"I am much obliged to you for your kind letter of the 27th instant, and the favourable sentiments you are pleased to entertain concerning the designs of Providence, in raising me to my present station. May it please God to enable me to answer the honourable expectations of the genuine friends of liberty, and especially the pious hopes of the real friends of Zion.
"To have prefaced the confederation with a decent acknowledgment of the superintending Providence of God, and his conspicuous interposition in our behalf, had doubtless been highly becoming a people so peculiarly favoured by Heaven as the Americans have hitherto been. But any article in the confederacy respecting religion was, I suppose, never in contemplation. The States being severally independent as to legislation and government, tho' connected by the federal league for mutual benefit, were presumed to have formed a political constitution to their own liking, and to have made such provision for religion as was most agreeable to the sentiments of their respective citizens ; and to have made the 'law of the eternal God, as contained in the sacred Scriptures, of the Old and New Testament, the supreme law of the United States,' would, I conceive, have laid the foundation of endless altercation and dispute, as the very first question that would have arisen upon that article would be, whether we were bound by the ceremonial as well as the moral law, delivered by Moses to the people of Israel. Should we confine ourselves to the law of God, as contained in the Scriptures of the New Testament (which is undoubtedly obligatory upon all Christians), there would still have been endless disputes about the construction of the of these laws. Shall the meaning be ascertained by every individual for himself, or by public authority? If the first, all human laws respecting the subject are merely nugatory; if the latter, government must assume the detestable power of Henry the Eighth, and enforce their own interpretations with pains and penalties.
"For your second article, I think there could be no occasion in the confederacy, provision having been made to prevent all such claim by the particular constitution of each State, and the Congress, as such, having no right to interfere with the internal police of any branch of the league, farther than is stipulated by the confederation.
"To the effect of part of your third article, that of promoting purity of manners, all legislators and magistrates are bound by a superior obligation to that of any vote or compact of their own; and the inseparable connexion between the morals of the people and the good of society will compel them to pay due attention to external regularity and decorum; but true piety again has never been agreed upon by mankind, and I should not be willing that any human tribunal should settle its definition for me.
"I am, &c.