That’s an interesting thought and you could potentially even do that using commodity hardware.
You could create a sound file which first plays a few short beeps for synchronisation and then does a sweep of the full frequency range. You’d then play that file back in macOS and in Linux at the same volume and record it with a mic in a fixed position.
Then you’d take the two recordings, line them up using the synchronisation beeps and compare the amplitudes of any given frequency. From that difference you could infer the EQ you’d have to add on Linux to get the same frequency response as macOS.
I don’t know how exactly you’d do the last step but it should at least be possible.
Mic quality (beyond a very basic point) or colouring should be an issue since you’d have the same mic frequency response in both tests and only care about the difference.