I guess part of the stereotype that ancient peoples had brown clothes must be from the fact that even when the clothes get preserved, which is very rare and biased towards certain materials more than others, the dyes of course won't. here's a 2000-year-old outfit found in the peat in Huldremose, in today's Denmark; a reconstruction from the Nationalmuseet of what it would have looked like when the woman wore it (https://en.natmus.dk/historical-knowledge/denmark/prehistoric-period-until-1050-ad/the-early-iron-age/the-woman-from-huldremose/the-huldremose-womans-clothes/); and a recreation with period materials by youtuber Sally Pointer (https://www.youtube.com/watch?v=vnAXYrcKVEE )