You're right, that would be more appropriate. I don't understand why they kill animals when they are supposed to be protectors of the forest! It doesn't make sense. Maybe those aren't real furs?
By the way, the fact that they don't worship beasts is definitely true. They already worship Silvanne, so where else would they put totems?

Unicorns are spirits of nature, and therefore they are sacred to all Elven society. They are considered the totem animal of all Irollan, for it is prophesied that when the last Unicorn dies, Irollan - the Elven Kingdom - and all its inhabitants will perish as well. Although the truth of this legend is unknown to anyone, the shimmering aura of Unicorns endows them with the ability to shield their allies from enemy spells.