To control mute of FX using MIDI, the documented messages work great. 
For example:
Mute FX1:
B0 63 00 B0 62 51 B0 06 00 B0 26 00
Unmute FX2:
B0 63 00 B0 62 52 B0 06 00 B0 26 01
But as soon as an FX is configured to be inserted, it stops working - even though the same messages are sent, the FX stops reacting and so the mix can no longer be controlled over MIDI. 
What am I doing wrong?
Yes this is normal behavior and might not be a bug.
It was already reported.
A feature suggestion was already input ( cannot remember where).
Thanks, I’d really like to hear A&H’s rationale for why that would be normal behavior. Personally, I believe it’s unintentional on their part.
This is inherent in how the insert works, you loose direct control of input and output levels and mute. It is exactly the same on SQ, I have just tried it with my SQRack!
To illustrate:
When using Shared mode, there are essentially MIDI commands for a Mute button - either in the FX Send mix or the FX Return channel (red).
When using Inserted mode, these buttons aren’t even in the signal flow (yellow).
What might help here are, among other things, MIDI commands for FX In/Out.
Quite clear from a signal chain perspective. But from a usability view I think shared FX Mute achieves the same result as inserted FX In-Out - namely to turn the FX on and off. And unless there is a MIDI command to toggle between inserted/shared (pretty sure the answer is no) it makes sense that the the same MIDI command that controls shared FX mute, controls inserted FX in-out.
Can we try to find that feature request if there is one, thanks. Otherwise I will file one.
I think this the one:
Haha, from myself. 
Yes, that would be one way to solve it, since softkeys are available over MIDI. The downside though, is that an absolute state cannot me set - softkeys only offer ”blind” toggle in this regard.
I created this new suggestion: Add MIDI message to toggle Inserted FX in/out
Maybe I am thinking of this incorrectly as my brain is a little addled at the moment, but surely if you were turn OFF, or MUTE something that is inserted, it would then result in all signal being muted since there is no way for the signal to return through?
Surely setting up a midi command to bypass the inserted FX (as SQUser suggested) would be more beneficial, as this would basically “remove” the insert from the chain allowing signal to flow through the channel as normal.
