Ethernet (100 Mb/s) through relays
Ethernet is surprisingly robust and you can use surprisingly bad cables before it starts to fail. So to send data through would probably work quite ok.

But when you switch the relays you would end up with a disconnect and a reconnect and those could cause the connected devices to behave strange since you on a logical level "moved the cable" from one device into another in a ms or so. And I am not sure how they would react to that...

But I get the feeling that there is another solution to your problem that will work better, even if this probably will work.