Very well put! And the same is true of quantum theory too. And believe me, physicists are even more keen on questioning the postulates of QM because they are genuinely uncomfortable – but QM works fantastically well, including Bell-test experiments.
While it is true that constancy of the speed of light is an axiom in Special Relativity, it is a thorough misunderstanding of how physics works to contend that physicists believe it BECAUSE it is structurally an axiom in the theory. Physicists believe it because it corresponds to the way nature is observed to behave. We don't dismiss alternative theories because they would break all our theoretical structures (although they do that), but because they almost always immediately fall into contradiction with measurements. We have looked really hard for violations of Lorentz invariance, and the experimental bounds are brutal. If it's there, it is extraordinarily tiny.
It is also a misunderstanding to contend that physicists are unwilling to consider alternatives. There are lots of papers on variable speed of light theories, and even some cosmological observations supporting time-dependence of the fine structure constant. I have personally written multiple papers on superluminal aethers that allow FTL signal propagation without violation of relativity. The papers are out there, but knowing that requires actual work, whereas portraying physicists as dogmatic, closed-minded sheeple on social media is free.