I wrote my thesis on this subject. I wasn't able to secure a copy of this book until about halfway through the research process. It was thus disspiriting to find, when I got it, that Stauffer had already covered most of the ground I hoped to. His account is fairly comprehensive, and is the only such account ever published of this interesting episode.
The story here is that a group of New England preachers in 1798 made inflamatory accusations of certain unnamed countrymen. They alleged that a secret, subversive organization had been moving all the tumultuous events in Europe since 1789. They alleged that this organization was now operating in the United States, with the support of treacherous Americans. This organization was said to seek the overturning of religion, abolition of property, free love, and so on.
The big players in the affair were Jedidiah Morse and Timothy Dwight, a pastor and a college president. Morse introduced the charges, publicizing conspiracy theories from Europe, and suggesting that they explained domestic events too well for it to be coincidental. These charges made the rounds through dozens of sermons and Thanksgiving Day orations throughout late 1798 and early 1799. Morse inadvertently brought the controversy to an end when he promised to reveal a list of Illuminati members residing in the United States. When he then came forth with a list of French masons who had fled the revolutionary violence in Haiti -- hardly the most plausible subversives -- his argument became a laughing stock.
The scare fed on the diplomatic crisis and quasi-war with France in 1798 and 1799, and the hyperpartisan atmosphere that prevailed. It also fed on the churchmen's anxiety about several trends underway: the waning religiosity of Americans in the early republic; the open expression of deist and atheistic notions in widely distributed publications; the ascendency of liberal theological readings at the expense of Calvinist dogma; and the political opposition to the established state churches in New England. (Most states originally had an established state church, which was supported through subsidies and/or compulsory attendance and tithing laws. This became unpopular.) With enemies on all sides, conservative New Englanders adopted conspiratorial interpretations that were being promulgated by English and French reactionaries.
The New England expression of this conspiracy theory was imbued with millenialism. Many of the orations that contained accusations of conspiracy also contained lengthy interpretation of recent events, matching them to the book of Revelations. They often suggested that the novelty of the events of the 1790s foretold an imminent return of Christ.
Short term, the people associated with the Illuminati scare lost on almost all counts. They failed to substantiate their allegations. They failed to stem the spread of liberal theology. They failed to save the established churches in New England, all of which had been disestablished by the 1820s. Franco-American relations cooled down and full-scale war was avoided. Power changed hands peacefully, without massive unrest or radical consequences. In the longer term, however, the same set of people was associated with the Second Great Awakening, which reignited the evangelical spirit in the 1810s, spreading a theatrical brand of protestantism through the country. Expression of irreligious ideas became once again indecent. Unlike in Europe, secularism has since had limited success in the United States. Religiosity in public life is still seen as appropriate and becoming. This may be the true legacy of the men behind the Illuminati scare.