Comment by microtonal

I think you are confused. You can have a Linux distribution with software with incompatible licenses (e.g. GPLv2 and Apache License version 2), because the license for a particular program or library only applies to that specific work, not other works that it is distributed with. The GPL is very clear on this:

In addition, mere aggregation of another work not based on the Program with the Program (or with a work based on the Program) on a volume of a storage or distribution medium does not bring the other work under the scope of this License.

There are some cases where a separate work can be considered derivative and thus the GPL can apply. E.g. I think it is generally accepted that a program linked statically against a GPL library is considered a derivative work (and must thus must have a license compatible with the GPL). More controversial is whether dynamic linking creates a derivative work. To cover the latter case, a lot of copyleft libraries are licensed under the LGPL or the GPL with a dynamic linking exception.

At any rate, shipping a Linux distribution with GPLv2 code (e.g. the Linux kernel) and a GUI application that is under the Apache v2 license is not a problem at all (as long as the GUI application is not a derivative of a GPLv2 work).

(IANAL of course, so this is not legal advice.)