“Polyester (which is basically plastic) could be made into sheets instead of strings, so you don’t have to weave polyester. Wool, linen, cotton, etc have to be woven to make a begged. “
Those fabrics can be made into paper — in fact US currency is made from linen. So the same issues apply there.
I knew about the issue regarding plastic clothing and asked a shilah about wearing polyester mesh and the response was that we are machmir on treating ANY four cornered woven garment as a begged that needs tzitzit.