I would like to choose better, although there are times when needs or artistic requirements must. It is no get-out clause, just being realistic about how much choice there is about. My recent internet research shows that the choice is far greater than just a few years back.
It is not all about organic-not organic either. Just by buying linen instead of cotton, if it is practical, saves the environment. Linen has a shortish growing period from seed to fibre and doesn't need as many chemicals. It is also a plant, which grows in colder climates.
Wool is of course great, it comes from animals, which grow it again and again.
There is also the bamboo, growing at an unimaginable speed. I do not know how environmentally friendly the process of extracting the fibres from the bamboo is. Many eco-friendly firms seem to market the fibre, so I hope that it is OK.
Here are some links to the shops I have found. If you have others, please add in the comments and I will edit my list. The list is UK centred, but the shops send to other countries too.
Fair Trade Fabric sells fabrics and habedashery, both organic and fair trade! Good place to start.
Organic Cotton sells of course cotton, but also bamboo and linen fabrics. You can also buy organic sewing thread. They know personally the weavers of their fabrics! The site lay-out is slightly old-fashioned in my mind, but I don't care, they have great stuff to reasonable prices and it is fairly traded.
Ecotale sells linens sourced from European factories (less airmiles, no labour exploitation). They have a very informative site about how to choose the linen for your project.
Eco Earth has a vast array of undyed organic fabrics. There are a few coloured ones in between as well. You can even buy silk, which is made without harming the larva inside the cocoon. If you want to make your own cloth nappies, this is the site to visit. They have all the things for it, also FOLD OVER ELASTIC! I have had such hard time trying to find anybody selling this in the UK. They also sell fabric dyes suitable for the fibres in fabrics, so you can have these things with some colour.
Ray Stitch is not dedicated organic fabric store, but has a good choice of different types. It also has 100% wool felt in three different thickness and bamboo jersey.
The following shops are not dedicated organic/fair trade shops, but have in their collection organic prints. Just put "organic" in the search box, so you don't need to trawl through all the collections to decide which ones qualify.
Celtic Fusion fabrics
Saints and Pinners
The Eternal Maker Here you need to go "type of fabric" and choose organic.
There are over 200 different prints, so you are spoiled for the choice.
The fabrics in this post are all organic, as far as I remember. Most of them are out of print, but there are equally cute things on the offer out there. Monaluna is responsible for the animal ones and they tend to have this type quirky prints, which melt my heart.