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Subject: Not all dashi is fish or meat-based!
Although very VERY rare and not many, some restaurants use kombu(kelp) or shitake mushroom based dashi. However, bonito dashi is overly popular. You're lucky if you find restaurants that serves vegetable based dashi...
Also...one warning regarding natto(fermented soy beans). It may be seasoned with dashi(again, bonito/fish).
Make sure to check it before ordering food that contain natto, just to be on the safer side...