The best replacement for polyester is cotton.

The best alternatives to polyester are rated as following:
★★★★★  cotton
★★★★★  nylon carpet
★★★★  nylon
★★  wool
★★  cotton sheets
★★  polypropylene
★★  epoxy resin
★★  nylon flag
★  acrylic
★  epoxy
★  wool suit
★  microfiber
★  polyurethane
★  rayon
★  nylon luggage
★  nylon thread
★  cotton thread
  cotton comforter
  nylon paint brush
  silk
  lycra swimsuit
  nylon flags
  wool rugs
  nylon swimsuit
  fleece
  satin
  cotton warmer
  nylon carpeting
  rayon embroidery thread
  cotton socks
  nylon paracord
  polypropylene capacitors
  polyethylene
  nylon warmer
  polyamide
  down
  cotton shirts
  nylon paint brushes
  cotton comforters
  rayon fabric
  nylon rope
  silk tie
  cotton underwear
  cotton fabric
  polyether
  olefin
  nylon swimsuits

Your alternative for polyester is not listed? Suggest!
Speaking about polyester, one probably shouldn't forget about spandex.

Other search terms related to polyester and their ratings are:
★★★★★ spandex
★★★★ rit
★★★★ cotton
★★ rit dye
You have in mind a companion for polyester and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of polyester in all years. Click on graph for more.
polyester
cotton
nylon carpet