Is washing soda an eco safe alternative to automatic dishwasher detergent?

Yes, washing soda (sodium carbonate) is environmentally safe. Sodium is ubiquitous in the environment; it is one of the ions that make up table salt, as well as being a component of sand and many other minerals. Carbonate is found in limestone and some other minerals. The main contribution of sodium carbonate to washing (whether dishes, clothes, or whatever) is to increase the pH (make the water more basic) so as to help convert fats to soaps. It does this job better if mixed with equal parts of borax (as in twenty mule team).