I have been in many textile plants, and not seen much in the way of classified areas.
I don't think you can make a general statement about such a facility. If I were to hazard a guess, I would say that with good housekeeping you might be able to avoid classifying it. But there might be some pieces that present a special hazard.
The main hazard is probably fibers flying around, but usually there are not all that many of them and as long as they are cleaned up they probably don't present a hazard.
I did run into a control panel down in Mexico that caught on fire from cotton dust accumulations though. But it was because rather than cleaning the air filter that brought air into the cabinet, they removed it and cotton dust collected in the cabinet over time and eventually ignited.