Classical mechanics conformed to observations and could be confirmed by various tests. This led to widespread adoption until, observations were be made that did not fit the theories.

This is what I call the naive history of science. In this view science progresses inevitably because it relies on a recipe for doing good science (the scientific method). You could probably find this in a physics textbook, but these kinds of stories aren't taken seriously by historians of science.

Classical mechanics made incorrect predictions from the get-go (for instance it couldn't explain the observed motion of the moon), in addition to positing occult forces which many natural philosophers (especially on The Continent) believed were a return to the natural magic tradition. The disagreement over classical mechanics was not a simple problem of applying a method. There were deep metaphysical commitments that explain why some accepted Newton's theories and others rejected them. Theories "fitting" or "not fitting" observation cannot explain the history of physics (let alone the history of science).