This can be tricky because they are used interchangeably quite a bit in related conversations. The main difference is basically ownership.
In Linux, the main shell is bash.
On Linux, the main shell is bash.
Both mean almost the same exact thing and will be used interchangeably. However "In Linux" implies that bash is a part of Linux. "On Linux" implies you can use Linux to use bash. This specific instance is more complicated because of the fact that Linux is just a kernel, and the "virtual picture" of a OS we form in our heads.
If you look at a simple example using something else:
There is a rose on the plate.
There is a rose in the plate.
The first sentence makes it seem like a rose is on top of the plate. The second makes it seem like it's part of the plate.
So applying that back to your question, does "GNU/Linux" belong as part of (or a component of) "Free Software", or is it "a part related to." Because your trying to express that "GNU/Linux" is a part of the domain of "Free Software" in seems appropriate.