As that was a fairly interesting question, I decided to respond to it on my FAQ section.
The short answer:
Using the example of Artemis the huntress--I would have to respond, "Why is that Neo-Pagan choosing to specifically honor Artemis?"
There are numerous deities connected with the moon. Not all of them are associated with hunting. Why not choose another one?
The long answer:
Finding out why that specific Pagan--who is definitely opposed to hunting--presently is choosing to honor the Greek Goddess of the Moon and the Hunt. That answer will only give the rationale for doing so from the perspective of one Neo-Pagan.
Maybe that Pagan is honoring this deity because Artemis is protector of young maidens? Then, that individual is focusing on a particular attribute which is an important enough reason that s/he has decided to honor Artemis, in spite of being a hunting deity, too. In that case, s/he might say, "Well, I am honoring her because I want her to watch out for my 8 year old daughter at outdoor summer camp."
Maybe the Neo-Pagan is honoring this deity because Artemis is a protector of young animals? Artemis was "Potnia Theron" (Mistress of the Animals). According to one ancient myth, Artemis delayed some Greeks from sailing to Troy, because they had killed a hare and her young. Though Artemis is a Goddess of hunting, she was apparently angered because they did something hunters ought not to do--slaughter underage animals. Perhaps s/he loves this myth and honors Artemis because this deity is like a divine game warden, insisting that no one take more than the "limit" and within the proper age range.
This attitude isn't something unique to 20th/21st century Neo-Paganism. Many deities have been recognized as having more than one aspect or path. In ancient Greece, Artemis was invoked as Artemis Eileithyia by women giving birth. She was also invoked by women during the period of breast feeding infants. She was not invoked solely by the wives of men who hunted or by women who liked hunting.
Maybe you are thinking of a Neo-Pagan who is also a Vegan vegetarian, as well as being someone opposed to hunting? In other words, the individual doesn't want to eat meat and doesn't think a meat is "good" for humans.
I should point out think that any Neo-Pagan or Wiccan with half a brain ought to know that hares, as well as bunny rabbits, get eaten by owls, hawks, foxes, wolves, coyotes, bobcats, weasels, etc. There are lots and lots of natural predators hunting these animals.
I would think that a Neo-Pagan would know that Artemis is aware that little hares and bunny rabbits get eatten, too.
Artemis is Mistress of the Animals, all the animals--both hunters and hunted--are under her guardianship and benefaction.
Therefore, I don't see why someone wouldn't be able to honor Artemis with a libation of wine/juice/water and still choose not to personally hunt or eat meat. I don't believe that Artemis was ever represented as having only hunters and only omnivores among those giving her honor.
Let's look at this from another direction.
It is true that statistically many Neo-Pagans don't hunt. However that doesn't mean that all Neo-Pagans who don't hunt are opposed to all hunting. Those who are against hunting might only be opposed to humans hunting non-game animals, like song birds. Or might only be opposed to humans hunting out of season and/or without a licence. Or hunting in residential areas or game preserves. Or hunting animals on an endangered species list. Etc.
Perhaps I can clairfy this idea a bit.
I don't hunt. I never want to go hunting. I never want to shoot a rabbit or gut a deer.
Nevertheless, I don't find anything morally reprehensible in those activities. I just do not want to do it anymore than I want to go skiing or mountain climbing.
I like Artemis--but I don't feel I have to hunt to in order to honor her.
I decided to ask my spouse his opinion on this. His answer was suscinct. "If you don't want to hunt, stay home. Leave the hunting to Her."
Then he added, "Fortunately... if someone is having a hard time with a deity's or spirit's attributes then that Neo-Pagan can simply not use that deity or spirit."
He's quite right about that. Indeed, if someone has a problem with the Moon Goddess Artemis, s/he may prefer to invoke another deity with lunar associations. Kwan Yin. Kwan Yin does have connections to Wicca, as well as being a Chinese Bodhisattva. She is also revered by Taoists as an Immortal. In the West, she is called the Goddess of Mercy. She's a vegetarian and encourages her devotees to be vegetarian.
copyright 2012 Myth Woodling