Shredded bits of material under my trainer I'm starting to get a pile of what looks like tire rubber under my trainer. Could it be something else like dry chain lube coming off? Is this normal? Have I set up my trainer incorrectly? Do I just have to accept that my rear tire will need replacing in the spring?
Yes, its tyre rubber.
People typically use either old/worn, cheap hard compound or dedicated turbo tyres for this reason with wheel on style trainers.
The bad news is that more typically sprays off backwards than down on the mat where you see it, so there's a good chance the rest of your room has a light coating of rubber particles too!