I had the same problem and it drove me mad trying to figure out how to fix it. Thought I’d save everyone else the headache.
I searched the net for this problem, and had decided that Mute and Solo don’t work in Final Cut – well, actually, they work fine, unless you don’t know how Final Cut processes audio.
Mute and solo won’t work if you have ANY RENDERED AUDIO in your timeline. What you hear is not coming from the tracks themselves but from the Audio Render files.
Tips to fix.
In render manager delete all your audio preview files.
Try disabling audio on as many tracks as you need to get the active number of tracks down to 5 (depends on your system, some systems can handle less, some more, but on the average…most systems are limited to 5-7).
Try temporarily disabling any foreign format audio (audio that needs to be rendered in order to playback in that specific sequence with those settings)
Try exporting any such audio that needs to be rendered out to an aif file with the same sample rate and timebase settings as your sequence. Then re-import it, and replace the troublesome audio with the aif.
That should fix your problem