We use a lot of plastic bags in the CSA, for holding vegetables that need portioning, or are dirty, or shouldn't be rolling around loose in the bottom of the blue bag. I realize this isn't very environmentally-friendly. I've looked into waxed paper bags, which would resist the moisture from that lettuce head or those just-washed potatoes, but haven't found a good solution yet. So as an experiment last week I went ahead and tried out regular-old paper lunch sacks for the tomatoes, and so far it seems to be working.
There are a lot of environmental balancing acts in small scale farming and CSA distribution. The use of plastics is a big one, in packaging and in irrigation supplies. The use of fossil fuels is another, burned in tractors, mowers, and vehicles. We know that many people join CSA for environmental reasons, and it is true that you are doing better by the environment. But, this farm is still a product of the society in which we live. Paper and tin packaging is no longer used, I can't buy canvas irrigation hoses, and our world is measured at the scale of the car, not the horse. I drive a tractors a LOT on the farm, yet driving the vegetables to you accounts for 75% of the farm's fuel consumption. In fact, back-of-the-envelope calculation indicates that driving local vegetables to CSA stops and farmers' markets in small but inefficient farm vehicles consumes just as much fuel as it would take to truck food across the country in a packed 18-wheeler.
The biggest impact you have by joining the CSA may not be my farm's specific ecological footprint, but your choice to not participate in big agribusiness. I would say that it is large scale corporate enterprise that does the most ecological damage. By signing on with the small scale local business, it is your economic action that in fact does the most good for the plant–along with supporting the kind of society that you would like to see in the world--even if some fossil fuel gets burned to get those crops to your doorstep.