I am impractically frugal with fabric. I try to use up scraps whenever possible. There is a limit though. 1.5" square is as small as I will save, the rest goes in the trash, well, the sort of trash. I have a roundabout version of composting. I only use 100% natural fiber fabrics when I sew. Mostly cotton. I do this for the very reason that they can, in fact, be composted. I keep a separate trash can in my work room for actual trash and have found that only about 10% of my workroom waste is not compostable. Here's how it works -
I start with this - fabric bits and some torn up phone book pages from paper piecing. There's also some cardboard from packaging and such in there.
All of that then goes here. Where chickens do what chickens "doo." The fabric brightens up the coop a bit and gets mixed in with the straw and dust and all the lovely little microbes that help make compost happen.
Then it's off to the compost bin.
Where they'll be turned into some luscious compost for my tomatoes.