I didn't find anything on the FINA website that dictated what was considered a textile
This is exactly right. FINA doesn't have a rule specifically banning non-textile suits or non-permeable suits. Their new stance is that any new suit design needs to be approved, so it's sort of up to them what will be allowed. I'd say the chances a carbon fiber suit would be approved are close to nil.
I didn't find anything on the FINA website that dictated what was considered a textile
This is exactly right. FINA doesn't have a rule specifically banning non-textile suits or non-permeable suits. Their new stance is that any new suit design needs to be approved, so it's sort of up to them what will be allowed. I'd say the chances a carbon fiber suit would be approved are close to nil.
