In English, a vegetarian who eats eggs and dairy products can be referred to as an ovo-lacto vegetarian. By the same token, could a person who eats honey but is otherwise vegan be meaningfully called a mell-vegan?
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In Latin, 'honey' was mel, with the oblique stem of melli-. In English we generally use the oblique stem for Latin and Greek words, so the correct prefix would be melli-.
(Note: the genus of Honeyeater birds are the Meliphagidae, which unlike many biological names is from the Greek: meli- + phag-. Note the single l in the Greek form.)
Using the strict definition of vegan from when the term was coined in 1944, a person who eats honey isn't a vegan. This is different from the term ovo-lacto vegetarian because vegetarians are defined as "abstaining from the consumption of meat and by-products of animal slaughter", neither of which explicitly excludes eggs and milk. So an ovo-lacto vegetarian is still a true vegetarian, whereas a mellivegan isn't a vegan.
However, definitions change and the consumption of honey is debated within the vegan community, so a mellivegan can be considered a vegan.
You could call a honey-eating vegan a mellivorous vegans, since mellivorous exactly means honey-eating.
But wouldn’t honey-eating (or non–honey-eating) be good enough? I ask because I don’t think looking for a fancy word here is necessarily a good idea. You never want to confuse people on things like this, and fancy words will always confuse (some) people.
For example, I know non-mycophagous vegetarians, but they avoid describing themselves as such for fear of being fed food with (intentional) fungus in it.
Similarly, although most vegetarians will eat cheese only if is vegetarian cheese, since normally cheese is made with animal-derived rennet, it would not be helpful to invent a specialized technical term for this — and indeed might even be counterproductive.
It’s like how you never use fancy words to describe food allergies, for fear of feeding someone something one mustn’t. Best just to say what the deal is using simple words that everybody can understand without a classical dictionary on hand.