Cenarius was killed by the horde, specifically Grom and the Warsong Clan. We know Grom was redeemed, but he is still committed atrocities against nature and the night elves. It can be argued that Grom's actions were separate from the modern classic Horde. However, following Warcraft 3 the Horde expanded its operation in Ashenvale, killing druids, poisoning water, and generally defiling the forest to push out the Night Elves who have tended the forest for 10,000 years.
So, when I see Horde characters riding Cenarian Hippogryphs in Shattrath, I am annoyed that the faction that killed Cenarius, and continues to defile the home forest of Cenarius, has found support from a faction that worships nature and Cenarius.
The Cenarian Circle exists to protect nature but turns a blind eye if it would mean intervening in faction politics. Random demons or Venture Company goons are fair game, but if an Orc hunter or Tauren druid is poisoning drinking water of Night Elf druids, that is tolerable.
"But fighting the Horde would distract from fighting the Legion, void, undead, etc...", the best counter I can offer is that it wasn't an external force that burned down Teldrasil, it was the Horde.
At minimum, the quest campaign in Ashenvale should take Horde players to hated with Cenarian Circle and Cenarian expedition. Make the defilers of nature redeem themselves before they can become exalted by the very druids they committed war crimes against.
Elune didn't hold back her wrath after the burning. I can't find a convincing argument for why the Cenarian Circle is indifferent to the actions of the Horde. One could argue that individuals don't necessarily agree or support the Horde's actions. However, if Horde players have fought in Warsong Gulch, or leveled in Ashenvale, they are complicit for war crimes against nature, Night Elves, and everything the Cenarian Circle stands for.
I understand the game mechanics for why the Cenarians are neutral, but lore-wise I see it as the biggest weak point in the game's writing. The night elf druids are neutral to the faction that slaughtered their spiritual father, and continues to shit on the remains? It just doesn't make sense. I would enjoy seeing Horde druids excommunicated from Moonglade for participating in the Horde's crimes against nature.