So I was at the vet the other day, and he looked at my brand-new fleece-lined pouch and told me that synthetic materials are dangerous because they might get their feet tangled up in it. He said cotton was the best material to use. Has anyone had problems with fleece? Is there anywhere to buy pouches that doesn't use fleece?

Fleece has shown to be the safest fabric for gliders. You do need to keep their nails trimmed but because fleece doesn't unravel into strings, it is much much safer then other fabrics.
Cotton would be nice but they unravel causing strings that can wrap around the glider causing injury.

Even with fleece, you do need to do daily inspections of their pouches and other things to check for safety.

I've always heard that fleece is safer than cotton or any other fabric too.

maybe the vet was thinking of the fake fur stuff? It is possible that lesser quality fleece may have a something toxic in it?

here is an interesting link:
http://www.sew-whats-new.com/culshaw/fleecefacts.shtml