int x = PyOS_mystricmp("foo", "none");
expected: x < 0
actual:   x == 0

    while (*s1 && (tolower((unsigned)*s1++) == tolower((unsigned)*s2++))) {
        ;
    }
    return (tolower((unsigned)*s1) - tolower((unsigned)*s2));

The while-loop is finished when *s1 != *s2 (ex. *s1 == 'f', *s2 == 'n'), but s1 and s2 already point to next characters (ex. *s1 == 'o', *s2 == 'o'), so PyOS_mystricmp returns difference between these characters.

I didn't know PyOS_mystrnicmp() and PyOS_mystricmp() functions! They are not used in Python source code. They are not documented, but they are exported in pystrcmp.h which is included in the main Python.h header.

Also, they aren't safe with the Turkish "i".

You can find PyOS_stricmp from here:
  https://docs.python.org/3/c-api/conversion.html

And PyOS_stricmp is PyOS_mystricmp when MS_WINDOWS is not defined.

Include/pystrcmp.h:
#ifdef MS_WINDOWS
#define PyOS_strnicmp strnicmp
#define PyOS_stricmp stricmp
#else
#define PyOS_strnicmp PyOS_mystrnicmp
#define PyOS_stricmp PyOS_mystricmp
#endif

Unfortunately they seem to be part of the stable ABI (#18603).

This was fixed under Issue 41524.