Washing action can be categorized into 4 main under categories. The first two categories can be named as consumption of energy and water. In addition to this, the feature of fabric and chemical treatment( Detergents etc..) can be named under greenwashing.
For an school project,in 2005, i made a small research about laundry chemicals and i found www.sevethgeneration.com . Maybe you can check their internet site.
Also, there are some fabrics built with nanotechnology that is not getting dirty easily. In one research in Clemson University, researchers developed a coating method for fabrics with silver(Ag) particles. I am sorry that i couldnt find the web link but you can find it easily.
There are some white goods companies that produce energy and water efficiency washing machines. Some of these companies also focus on the warranty time in order to show the other side of sustainability and green concept in their commercial. For instance, Vestel ( a Turkish Manufacturer) gives 5 year warranty while the others generally give 2-3 years.
As KQD said, green- blabla can turn into a kind of consumption movement. On the other hand, i believe that these kind of products has great influence on the user. Changing behavior and habits will always take time. It is not only just fixing your product or using biodegradable toilet papers.
If user will care about their clothes and wear his clothes more carefully, not having sports (?) or forbidding kids to jump in mud (?) or being naked (?). It will be good for green-washing. The main problem is we need to decide logically where we need to stop and open-minded for technological improvements.