I'm in a unique position of needing to play both bass and guitar through my KPA at live gigs. Both instrument inputs could be switched by midi using an ABCadabra, no problem.
BUT, I haven't been able to find a comparable option for the balanced output (xlr or trs) going to FOH that is midi capable.
I'm trying to make the switch as fast as possible and having the in and outs change with my patches would be best.
Any thoughts? 
Are you using the FX loop on your Kemper at all?
If you aren't, you could maybe set up your bass patches with the FX send in X and something to completely mute your volume in Mod? Assuming you're able to find a stomp that mutes it (4:1 gate turned all the way up, maybe?) the Kemper would handle switching for you.
If you use a full range cabinet, you would not need to switch outputs.
Switching inputs can be done with any A/B switch.
IF you are even a little handy with a soldering gun, you could wire a DPDT switch to be a "dual" switch - it would do A/B and C/D at the same time.
OR - look for switch boxes made by WOBO - I'm sure he could make a dual switch for you. I have a "two in, two out, with switchable FX loop" box that he made on my live pedalboard, and it has been perfect for years 
Lokasenna - I'll check into that and see if it will work, even more cost effective than the way I was thinking
Paults - Your right about the cab, but I need a solution for sending two separate signals to the FOH mixer (one for my bass rigs and one for guitar rigs), preferably using MIDI so I don't have to flip any switches manually. That way they could be switched automatically when I change my rigs. Yes, I'm THAT lazy 
