With "stable core" I mean the kernel, grub, init system, x server, audio server, et cetera. Basically everything that is essential for the OS to function.
Some distributions that I have looked into:
It uses a purely functional package manager called Nix. Purely functional means that it will never modify an existing package, and old and new packages can live side-by-side, therefore allowing me to keep my core stable and only update user-software.
This seems like the best candidate, however, NixOS is considered experimental and under development, so currently this isn't an option for me.
I have read about BSD's and I have tried FreeBSD -- which seems to do exactly what I want -- separate the core from user applications.
Unfortunately, BSD's are not an option for me either, as AMD doesn't support their fglrx on them.
While the core is stable, so are the user applications (therefore old as well). I need the latest and greatest user applications.
I have used Debian backports before, but it doesn't contain everything I need, and from what I've read it could update the "core" if a package does require a new version.
I have also looked into CentOS, but from my limited experience with it, it seems very similar to Debian stable. Ubuntu/Fedora/OpenSUSE aren't options for me, as their cores aren't stable.
In case anyone finds this via. Google, I will add my progress, as I am sure I'm not the only one having this specific need.
After some research I have found schroot/debootstrap, which seems like a workaround I can live with for Debian. Debootstrap basically allows you to install another Debian system in a subdirectory. For instance, you install Debian stable as an OS and setup everything you need (grub/xserver/desktop environment/audio server/et cetera), and the rest, like user software you install in your home, which will be using the testing or unstable repositories.
Link to Debootstrap: http://wiki.debian.org/Debootstrap
Like this it is possible to have a system as stable as a server, with the latest and greatest software.
I have yet to find out how feasible this in practice.