OK, so this seems pretty obvious to me that natural dyes would be better for the environment than chemical dyes, but as Elizabeth Barrett Browning wrote in her sonnet: "... let me count the ways".
Chemical/ hazardous waste generated in creating chemical dyes & how to dispose of them.
Studio chemical dye waste and how to dispose of that. When I began dyeing in the studio, I began with acid dyes, but the colors were too brash for me and waste dye disposal was a problem.
3. All of the transportation, potential spillage and groundwater contamination that comes with large-scale chemical manufacturing.
4. Health effects of concentrating chemical production in geographic areas (urban or rural) that have other economic/ racial/ social challenges.
5. Social justice and fair wages... I am a fiber artist/ crafts-person and I am committed to paying my studio assistants a living wage, but business models for Artists is another topic.
Needless to say, all of these issues are vastly reduced or eliminated in natural dyeing, especially if you avoid the toxic metal-salt mordants (copper, tin, etc.), as I do. My waste baths, I pour in the garden. I am careful about fumes - even with plants harvested in my yard. My dye studio is very small scale... I do use electricity & propane, I do use ubiquitous chemicals (ferrous sulfate solution, for example, but there is so much iron in my Virginia soils, already!) In another post, I'll tell you where I get my dyes...