I suspect the day will come where we have new high-tech options for sails that are made of friendlier renewable materials. Until then I suspect polyester sailcloth is the best choice. Although it is easy to look at Polyester as an unfriendly product because it is made form non-renewable fossil fuels, with some thought it has features that can offset this.
1) It is very long-lived in a junk sail. Depending on use, a decade seems reasonable. I didn't even consider cotton because I was completely unfamiliar with cotton sails and all that I had read suggested that you couldn't expect anywhere near the durability or performance of polyester. Remember sail performance also counts, good sails mean less motoring.
2) Polyester sailcloth can be recycled and reused. There are now quite a few folks remaking sailcloth into all sorts of consumer goods after its first life as a sail. Most of this is from short-lived racing sails, but if there is good cloth left in your sails when you replace them, there is nothing to stop you or someone else from putting it to productive use.
3) Ordering factory seconds like David suggests makes huge sense. If there is not a market for these materials the manufacturer has to dispose of the material, with obvious negative impacts.
4) Consider where the sailcloth is made, polyester sailcloth made in the EU is going to have a smaller ecological footprint than something made in china where the same kind of environmental protections are not in place.
5) Buy the best fabric you can. Although figuring out the exact footprint of a material is complex, usually a good way to reduce the impact of a material is to buy the one with the greatest longevity. For me, I chose to use the real sailcloth, because I felt that with a sailcover it would give the greatest longevity. One of the sailcloth experiments that seems not to have worked is Odyssey. The short lifespan a number of users have had with this material put it in the ecologically unfriendly category.
6) Use a sailcover. Regardless of which synthetic you use, a sailcover is going to protect if from UV and extend its life and therefore reduce its impact. I have no idea what the best care would be for a cotton sail to extend its life. Somehow you have to wait until it is dry to put the sailcover on? I live in Vancouver!!!
7) Use dark coloured cloth. Although the addition of UV inhibitors matters a lot, generally speaking the darker the colour of a synthetic material the better its UV resistance.
8) There are lots of used sails around that could maybe be re-cut into a junk sail. This would be a bit labour intensive and pointy sails don't provide the greatest geometry in terms of making panels for a junk sail. But, if you used vertically seamed panels, you could likely make it work. You'd probably have a few different weights of sailcloth from the different bermudan sails you'd need to use and could use the heaviest weight material for the top of the junk sail (storm sail) and the lightest weight material for the bottom (fills with wind more easily).