In his very important discussion of Isis and Osiris in his collection of essays Moralia, Plutarch discusses the reason that the priests of Isis wear linen garments.  He writes:
It is true that most people are unaware of this very ordinary and minor matter: the reason why the priests remove their hair and wear linen garments.  Some persons do not care at all to have any knowledge about such things, while others say that the priests, because they revere the sheep, abstain from using its wool, as well as its flesh; and that they shave their heads as a sign of mourning, and that they wear their linen garments because of the colour which the flax displays when in bloom, and which is like to the heavenly azure which enfolds the universe.  But for all this there is only one true reason, which is to be found in the words of Plato: "for the Impure to touch the Pure is contrary to divine ordinance."  No surplus left over from food and no excrementitious matter is pure and clean; and it is from forms of surplus that wool, fur, hair, and nails originate and grow.  So it would be ridiculous that these persons in their holy living should remove their own hair by shaving and making their bodies smooth all over, and then should put on and wear the hair of domestic animals.  We should believe that when Hesiod said,
Cut not the sere from the green when you honour the gods with full feasting,
Paring with glittering steel the member that hath the five branches,
he was teaching that men should be clean of such things when they keep high festival, and they should not amid the actual ceremonies engage in clearing away and removing any sort of surplus matter.  But the flax springs from the earth which is immortal; it yields edible seeds, and supplies a plain and cleanly clothing, which does not oppress by the weight required for warmth.  It is suitable for every season and, as they say, is the least apt to breed lice; but this topic is treated elsewhere.
From the Frank Cole Babbitt translation published in 1936 in the Loeb Classical Library, available online here.
Note that among the possible reasons that Plutarch says people give (but which he says are incorrect) for the priests' refusal to wear wool is "because they revere the sheep," which may be referring to terrestrial sheep but may also be referring to the heavenly sheep found in the zodiac, which we know as the constellation Aries.  In the passage above, however, Plutarch refutes those other reasons (at least he seems to refute them), and argues that the real reason that the priests of Isis do not wear fabrics made from the hair or wool of other creatures has to do with a belief about the nature of matter and the body, no doubt having to do with a particular doctrine about the sojourn of the soul and spirit within the fleshly material of this world, and from their desire to avoid routine contact with and contamination from "excrementitious matter" (either by wearing it or by eating it).

Interestingly enough, in a recent interview on "Radio 3Fourteen" (a production of Red Ice Creations), Lana Lokteff interviews Brian and Anna Marie Clement, of the Hippocrates Institute, and during the interview they give their opinion that among natural fibers to wear as clothing, linen is one of the best!

In that interview, Brian and Anna Marie Clement present evidence that synthetic clothing, often made from petrochemicals and treated with other powerful chemicals and dyed and coloured with still more chemicals, are very damaging to the environment during manufacturing, can have detrimental health effects on the body and brain, and can potentially "off-gas" chemicals for years and years after being first worn.

Reading up on the processes used to produce synthetic fibers does confirm the routine use of some pretty powerful chemicals.  For instance, one of the steps in the production of acrylic fibers may include dissolving polymers in a solution of N,N-dimethylformamide, which some believe can be linked to cancer in humans.  The production of spandex generally requires the mixing of a macroglycol with a di-isocyanate monomer -- and isocyanates are made by treating amines with phosgene, a poisonous gas which was infamously used as a chemical weapon during the First World War.

Brian and Anna Marie Clement instead recommend seeking out clothing made from organic materials (such as silk or linen) and manufactured using natural processes.  For more information on their views and research on this topic, see their 2011 book, Killer Clothes.

In a different essay, "On the eating of flesh," Plutarch argued that eating meat was a form of "slandering the earth" by implying that "she cannot support you" with the grains, fruits and vegetables that grow for food, asking:
Why slander the earth by implying that she cannot support you?  Why impiously offend law-giving Demeter and bring shame upon Dionysus, lord of the cultivated vine, the gracious one, as if you did not receive enough from their hands?
Perhaps he would use the same arguments for the creation of synthetic fabrics, had he known of such things, asking the same questions and arguing that nylon and rayon and polyester indicate a lack of faith in the earth to provide natural fibers for our clothing.

In any event, it is interesting to consider Plutarch's arguments for the wearing of linen, which "supplies a plain and cleanly clothing."