> The MSVC linker is apparently much more lax in this regard.
No, you are incorrect. The function in question was tagged as inline. Having multiple instances of it is legal. If a Unix linker gave an error on multiple copies of an inline function then that would be a serious bug that would prevent them from linking any non-trivial C++ program.
For inline functions it is only an ODR violation if the two instances are different in an ODR relevant way. The language spec doesn't discuss compiler switches but it is logically clear that /arch:AVX versus not is an ODR violation, whereas /O1 versus /O2 is not. So therefore, even having two different instances of a non-inlined inline function is not necessarily illegal, and must be accepted by a conforming linker.
> Use inline without explicit extern.
I'm not sure why you think that this is a solution. An explicit 'extern' is not needed when defining an inline function. If it is not inlined then the compiler generates a copy that can be referenced. I have worked with gcc, clang, and VC++ and I have never had to explicitly mark an inline function as extern.
You are correct that static inline solves the problem, although I think that this is an ugly solution. And, it is a standard library solution, rather than a toolchain solution, so it doesn't automatically help developers who write their own inline functions.
The best suggestion I heard (on twitter) was name mangling (for non-inlined inline functions) that added an architecture suffix, thus making accidentally calling the wrong architecture function impossible. Much cleaner and more efficient than static inline.