James Hutson in Church and State in America tells this story:
In 1798 John Adams experienced how inflammatory the exercise of a familiar religious act by a national official could be in a country that had been taught to cultivate and cherish republican jealousy. On March 23 of that year, when the nation was in the midst of a “quasi-war” with France, Adams proclaimed a national day of fasting and humiliation, a practice that American magistrates had followed since the earliest days of the seventeenth century. It so happened that the General Assembly of the Presbyterian Church was meeting in Philadelphia when Adams issues his proclamation. Though not a Presbyterian, Adams was branded one by his political opponents and was accused of scheming to rivet a Presbyterian establishment on the nation, the evidence being his fast day proclamation. “A general suspicion prevailed,” he wrote, “that the Presbyterian Church was ambitious and aimed at an establishment as a national church. I was represented as a Presbyterian and at the head of this political and ecclesiastical project.” The result of his fast day proclamation, Adams claimed, was his defeat in the presidential election of 1800.
Hutson gives evidence why Americans should never have suspected that Presbyterians would be the national church. The reason is that their theology was entirely incompatible with one of the major reasons the founders gave for religion being important to a free society. According to Rev. Samuel West, of Massachusetts:
perhaps no one if of greater importance to promote the peace and safety of the community than the doctrine of a future state of reward and punishment; for we shall find that persons are often restrained from gross immoralities by the fear of future miseries, when civil penalties prove insufficient for that purpose. A doctrine of such amazing importance to promote the civil good of society ought to be very strongly impress’d upon the minds of men in order to render it beneficial to society. (111)
Since Presbyterians and Lutherans who trusted Christ no longer feared future punishments, they were immune to such incentives to civic virtue. In fact, Calvinism’s may have been a threat to civil society as republicans conceived it.