Are chemical fibers organic?

Yes

Chemical fiber is a kind of artificial synthetic organic matter. It is a fiber made from natural or synthetic polymer compounds through chemical and physical processing. Chemical fibers can be divided into two categories: man-made fibers and synthetic fibers. Man-made fibers are fibers made from organic polymer compounds synthesized through addition polymerization and polycondensation reactions using natural cellulose such as wood and pulp as raw materials. Synthetic fibers are fibers made of polymers, such as polyester, nylon, acrylic and spandex, which are synthesized from raw materials such as petroleum, natural gas and coal through complex chemical reactions.