clang++ and g++ are ABI incompatible, even for things as core as standard containers, according to, e.g., the clang++ website.
Debian ships with C++ shared libraries, i.e. libboost, etc... that are compiled with ~something and user programs using both compiler generally work, and the library names aren't mangled with the compiler that was used for them. When you install clang, debian doesn't go and pull in duplicate versions of every C++ library installed on your system.
What's the deal? Is the ability of clang to link against distro-provided C++ libraries just way stronger than the (thankfully cautious) compiler devs describe it to be?
even for things as core as standard containers
Standard containers are not all that "core". (For typical implementations) they are implemented entirely in valid C++ in headers, and if you compile the same headers with G++ and Clang++ you'll get ABI compatible output. You should only get incompatibilities "even for things as core as standard containers" if you use different versions of the container headers, not just by using Clang instead of GCC.
Both GCC and Clang conform to a cross-vendor, cross-platform C++ ABI (originally developed for the Itanium architecture, but also used for x86, x86_64, SPARC etc.) The really core things such as class layout, name mangling, exception handling, vtables etc. are specified by that ABI and Clang and GCC both follow it.
So in other words, if you compile the same source with GCC and Clang you'll get ABI-compatible binaries.
If you want to understand this stuff better see my What's an ABI and why is it so complicated? slides.