Linux is a general-purpose OS, and that is generally a bad choice for safety-critical real-time applications. And it is not something that Linux can just be adapted for – the biggest problems are: the kernel is big and the code is complex. Anything added do Linux to 'solve that' would just make it even bigger and even more complex. And removing stuff for kernel would just make it worse general-purpose OS.
The solution for proprietary RTOSes used there would be to create a new, open-source one. This should be doable as those are small and simple by definition (to some extent – only as simple as they can be for given task). I guess this will happen one day, though it is harder for it to happen naturally, as that is not something hobbyists would do for their own needs in their own time and that is usually what starts an open source projects.
On the other hand – Linux can co-exist and I am sure it does co-exist with those specialized RTOSes. I would assume that even on a Boeing airplane there are many Linux instances running… or even Windows ones.
VulcanSphere