An ABI, even for C, has parts which are quite platform independent, parts which depend on the processor (which registers should be saved, which are used for passing parameters,...) and parts which depend on the OS (more or less the same factors as for the processor as some choices are not imposed by the architecture but are the result of trade-offs, plus some OS's have a language independent notion of exception and so a compiler for any language has to generate the right thing to handle those, handling of threads may also impose things on the ABI -- if a register points to TLS, you can't use it for what you want).
In theory, every compiler may have its own ABI. But usually, for a couple processor/OS, the ABI is fixed by the OS vendor which often also provide a C compiler and common libraries which use that ABI and competitors prefer to be compatible. (I'd not be surprised if there are exceptions for some OS for which C isn't a major programming language).
But the OS vendor may switch ABI for one reason or the other (new versions of processors may have features that you want to use in the ABI for one - for instance some have asked for a 32bit ABI for x86_64 allowing to use all the registers). During the migration phase - which may be for a very long time - you may have to handle two ABI.
extern "C"
on everything you publish, and/or use the same compiler for linked executables. – Applesauce