I have not be as emotionally invested in "infinitesimals" "limit definition" and "Archimedean property" if these were not based on "Science is Settled" arguments that don't have logical basis.
(note: i don't deny that some areas of math are highly controversial like
ultrafinitism, which many view as Flat Earth is viewed by geologists)
The current mathematics structure is like a house of cards relying on
axioms that aren't acknowledged as axioms or proved by circular logic where proofs are relying on systems constructed using these axioms.
When a contradiction in a system is spotted, the usual reply that "its wrong due X"
ignores that X itself is a products of current system and alternatives to X don't exist or aren't developed(due lack of interest or paradigm dominance).