I've never heard anyone say any of these supposed myths, except for the first one, sort of, but nobody means what the first one pretends it means, so this whole post feels like a big strawman to me.
Also compiler optimizations should not affect the result. Specially without "fast-math/O3" (which arguably many people stupidly use nowadays, then complain).
-ffp-contract is annoying exception to that principle.
a couple of decades ago, I was still a lowly applied mathematics (and aspiring programmer) student when i proposed to a professor to change the compiler options from O2 to O3 to gain performance (reducing run time by a significant percentage like 50% or more...) only to be disregarded by saying "no, compiler optimizations break numerical accuracy".