Originally, the causality described by Aristotle is a concept that includes 4 causes and that aim to answer the question of "why" (Falcon, 2009). Among the 4 causes, the final or teleological cause ("the end", "that for the sake of which a thing is done") acquired a cosmic connotation in the Middle Ages and became attached to the Judeo-Christian God (Greene, 1976). I deduce from this that, consequently, the Church had a say in matters of causality, if not an authority of divine right on the question, and therefore on any question given the broad scope of the concept of causality.
Pearl (2000) reports that Galileo advocates that physics should not be concerned with the "why" but with the "how" and thus with the Aristotelian notion of the efficient cause. He also points out that Galileo suggests that common language should even be abandoned in favor of algebra. Inasmuch as Galileo was under the wrath of the Inquisition, a legitimate question is: were his methodological choices and recommendations guided by the intention to protect himself from the criticism of the Church?
Besides, Galileo's case had a notable influence on Descartes. It discouraged him from publishing his physics and encouraged him instead to write a work that was poor in scientific fact, i.e., his method: a return to pure reason and common sense. In the same way as for Galileo, aren't Descartes' acts and the emphasis on the pure reason a response to religious dogmatism?
Finally, Newton, in his empirical approach formulated the famous phrase "hypotheses non fringo", I do not make hypotheses, basically hiding behind observational data and claiming that he had no opinion. Rather than promoting his method, isn't this also a way of protecting himself from criticism?
Thus, in different ways, are mechanistic thought, algebra, pure reason, or even data, all refuges or umbrellas to protect oneself from the dogmatism of the institutions that hold authority over what is judged true or false within a society?
I have always believed that these scientific methods/tools or principles were born and became popular because of their own merits. This is certainly true in part, but I remain a little confused that they may actually be a product of history associated with a political context and the desire to guard against it, and not for the sake of science itself. It suggests that science could have evolved differently without religious dogmatism.
Falcon, A.: Aristotle on Causality, in The Stanford Encyclopedia of Philosophy, edited by E. N. Zalta, Metaphysics Research Lab, Stanford University. [online] Available from: https://plato.stanford.edu/archives/spr2019/entries/aristotle-causality/
Grene, M. (1976). Aristotle and Modern Biology. Boston Studies in the Philosophy of Science, 3-36. doi:10.1007/978-94-010-1829-6_1
Pearl, J.: Causality: models, reasoning, and inference, Cambridge University Press, Cambridge, U.K.; New York, 2000.