This makes me wonder if we could also argue that there were multiple denominations of classical mechanics. Newton's laws, Hamiltonians and Lagrangians come to mind. I recall that people including Newton were also unsettled by Newton's law of gravity ('action at a distance')[1] and tried to come up with more 'intuitive' theories. The one where the law of attraction arises from being bombarded by particles from the universe (screening) was an amusing one that doesn't work due to thermal effects [2].
[1] https://en.wikipedia.org/wiki/Action_at_a_distance [2] https://en.wikipedia.org/wiki/Mechanical_explanations_of_gra...