A colleague made a cake for his birthday and brought it to share. He explained that it was “vegan and gluten free”. As legal editors do, we discussed whether that meant it was (vegan) and (gluten free) (probably) or (vegan free) and (gluten free) (probably not), and further what “vegan free food” might actually be (as opposed to “vegan, free food” (which would probably be “free, vegan food” anyway)).
The phrase can either be ADJ and N free or N and N free. Vegan can be a noun (My cousin is a vegan) or an adjective (?My cousin is vegan, This cake is vegan). Compare organic and preservative free and additive and preservative free. Hyphens might or might not help: organic and preservative-free, additive- and preservative-free, additive-free and preservative-free.