How can I multiplex fully isolated differential signals?
Relays are a very good solution, as all ports are isolated from each other, and the withstand voltage of the switches is high. They are DPDT so only one is required.
Look at NAIS TQ2 series. They are not expensive relative to multiple specialist optos. 
They can be held at low power, or use single coil latching if you need minimum energy.

Opto-fet isolators/switches are an easy solution to a lot of problems like this, if a relays are not. But your job needs a total of 4 switch contacts / fets, per channel pair. It will cost more than relays, and probably use more power, and have lower withstand voltage