The incredible scientific success of Isaac Newton led to intellectual revolutions in science, philosophy, economics, and theology. But many of the ideas developed and promoted have a dubious intellectual parentage.
The key issues to consider centre around whether Newton's approach, success and interpretations in physics translate to other topics of interest.
Newton studied a specific topic: the mechanical motion of bodies, including cannonballs and planets. He used a method appropriate to that topic. High levels of precision, both in measurement and in making theoretical predictions were possible. This led to high levels of certainty about what was true and what was not.
A few intellectual bastards fertilised, fed, and sustained by the success of Newtonian mechanics include the following.
People are machines.
Auguste Comte (1798-1857) was the first philosopher of modern science and a founder of sociology (social physics). He was the founder of positivism, claiming that societies progress through three stages: theological, metaphysical, and positive. These correspond to eras of primitive (Christendom), Enlightenment, and modern science. Comte promoted a hierarchy of sciences with physics as the most fundamental. Comte's legacy has been roundly criticised by Pierre de Gennes, a Nobel Laureate in Physics.
Foundationalism seeks to establish truth logically by starting from a few axioms that can be taken as self-evident or "justified". There are parallels to Newtonian physics in that it starts with just Newton's laws and can deduce all the details of mechanical motion from these laws.
Theology was diverted in unfruitful directions and impoverished by these intellectual movements that claimed credence because of the success of Newton. There was a desire to mimic methods and levels of certainty of Newtonian physics. Here I identify several problematic movements in theology.
Deism. This was a natural outgrowth of the clockwork universe.
Foundationalism. Theology is largely concerned with propositional truth rather than with godly living. The object-subject distinction was considered possible and desirable.
Liberal theology. Since one could not match the confident certainty of Newtonian science one was left with doubt about everything: the reliability of the Bible, miracles, the existence of a heavenly realm, and the divinity of Jesus. The solution was the methods of historical-biblical criticism (form, source, redaction, literary, .. criticism), demythologisation, ...
Fundamentalism. This reaction to liberal theology led in the opposite direction. A desire for certainty produced notions such as the infallibility of scripture, the inerrancy of scripture, and strict true-false dichotomies with little room for paradox, dialectic, imagination, or polyphonic readings of texts.
Modernist forms of apologetics. In the second half of the twentieth century in the U.S.A. , there was the development and promotion of evidential apologetics and presuppositional apologetics. They attempted to show the intellectual validity of orthodox faith to the point that anyone who did not believe or accept the arguments presented was portrayed as irrational. Presuppositional apologetics aims to show a non-Christian that their worldview is intellectually incoherent and then in their despair preach the gospel to them.
In conclusion, I do not think any of these movements was particularly helpful. They impoverished theology rather than enriching it. Their intellectual foundations were shaky. They created as many problems as solutions. They lacked nuance and in hindsight are now seen by many as problematic. Humans and the Triune God (Father, Son, and Holy Spirit) are not cannonballs or planets orbiting the sun like clockwork. The methods and certainty of Newton cannot be uncritically transposed onto other areas of knowledge.