The book's thesis is that there were two wings of the Enlightenment, the radical wing and the moderate wing. The radical wing more dominated France's revolution. And although the radical wing was well represented in the American Revolution (by among others Jefferson and Paine) the moderate wing more dominated.
Israel, as a British writer, focuses on Enlightenment as it relates to Western Civilization in general; as it were, the American Enlightenment is just a particular focus in a general movement. He has to deal with grasping a great many figures and Israel sometimes overstates his case or otherwise contentiously analyses historical facts; but on balance he grasps them well.
Regarding Enlightenment and religion, I was happy to see Israel notice (as I have) the special place "providential Deism" and "Christian Unitarianism" had among the Enlightenment thinkers. The book stresses Richard Price and Joseph Priestley to represent radical Enlightenment in England. And also for equal gender representation (an Enlightenment idea!) Mary Wollstonecraft and Catherine Macaulay.
Here is how he deals with Benjamin Rush, that American Enlightenment "Christian":
[H]e had been a fervent Evangelical as a young man. Yet his radical libertarianism stemmed not from this religious background (which he soon abandoned for a highly unconventional kind of Christianity), but from Enlightenment ideas that he avidly absorbed as a student in Edinburgh and in London and Paris in the years 1766-1769, when he met Hume, Ferguson, Diderot, ... Macaulay, and other Enlightenment figures. He switched to radical ideas because skepticism, having destroyed his confidence in conventional political notions, led him to suspect, as he put it, "error in everything" he had previously been taught in America.
... Rush became an advocate of liberty, equality, and fraternity in which all men would share. ... After returning to his homeland, Rush became a famous medical and political reformer, and in religion, from 1780, for some years an advocate of "Universalism" -- that is, the doctrine of universal salvation of souls irrespective of belief or behavior, the only theology that renders all souls equal and considers union between all the Christian denominations a necessity if "corrupted" Christianity is to be eradicated and mankind's interest promoted. Like the Unitarians, to whom he was close, Rush stressed one's obligations to the entire human race, opposing all theology dividing Christians into separate denominations. Aspiring to unify reason with religion, he proposed stripping away practically all traditional theology. (pp. 42-43.)
My biggest disappointment with the book is its, at times, abstruse prose. This is a problem from which many academic book suffer. Parts of the book could use a rewrite.