Things I have tried to fix the problem
1. Restart Client
No result
2. Remove all Modules and save loadout
Gives same error with modules removed.
3. Click "Strip" button and use "strip all modules" option
allowed me to save the mech with no Modules.
4. Added Modules back to mech.
Was able to save mech without error.
This was all reproducible multiple times. As you can see below however I did not change the Modules during the workaround. Just re applied them
Before workaround

After Workaround
