This is a great question and beyond my own depth in the Early Modern period. But I will note that Cartseianism actually was a problem for Newton. Cartesian philosophy (which was extremely popular in the late 17th century) argued against "occult" causes in favor of a purely mechanical approach to the universe. If you want to say something happened to something else, you can to outline exactly how that worked in a very mechanistic way. But Newton lacked such a mechanism for Gravity — it simply did affect things, but he didn't have a mechanical explanation (there were no gravity particles, for example; it was just "action at a distance"). This made its acceptance difficult and easy to criticize as an "occult" theory. Eventually the utility of Newton's approach outweighed these philosophical objections (and, indeed, we are still searching for mechanical explanations of gravity, in a sense — you can see the theories of quantum gravity as a modern-day extension of this search, whereas General Relativity by contrast just declared the problem irrelevant).

Going through my grad school notes, I find that I supposedly once read a book by Daniel Garber, Descartes Embodied: Reading Cartesian Philosophy Through Cartesian Science. I admit to totally forgetting all of it at this point (not really my bag), but if you are looking for follow-up, it might be a place to go. The book I do remember reading about Cartesian philosophy is Stephen Toulmin's Cosmopolis which is about comparing the rival philosophies of Descartes and Montaigne, and is more about the way the Cartesian worldview is impoverished by comparison (despite it having "won out" in the Enlightenment). On Newton and the Cartesians, it is mentioned by Kuhn in The Structure of Scientific Revolutions but if one wanted details I would look in Richard Westfall's Never at Rest, the definitive Newton biography.