Considering the fact that both Gwen's skirts and Benny's shirt were used to make bandages, I think it's safe to say that most clothing is made of
natural fibers. From Gwen's reaction to the Temple's garden, my money's on hydroponics as a source of fibers for clothing.
There are plenty of fiber producing plants that can serve double duty (the flax used to make linen, for example, may also be used to generate
linseed oil,
hemp plants also produce, shall we say, "medicinal" compounds, and apparently
sisal is so versatile it can even be used as a bio-fuel source).
Given the somewhat anachronistic setting, I wouldn't be surprised if
rayon was also out there; while it's cheapest when made from wood fiber, from what I read in the Wikipedia article, it can be made from any cellulose source.