> So what libraries have this property? I've read in old threads about even glibc making changes that break binary interface compatibility.

You can request different ABI versions from glibc. And glibc doesn’t introduce breaking changes every day but rather every few years.

Asides from rare bugs (which get fixed), glibc does not break ABI. However, glibc does extend the ABI with new versions so compatibility only goes one way - your runtime glibc (generally) needs to be at least as new as the one used for linking.