No, I don’t think so. Not any more than they hate orcs or trolls.
When you play Warcraft III ROC, where they were introduced, you can clearly see that they are painted as a mostly idyllic society based around harmony and closely integrated with the backstory from 10k years ago. Their lore essentially says they annihilated the troll kingdoms and saved the world from the Burning Legion (after Azshara brought them there, but that is effectively different from player faction).
I think what you’re seeing in modern post-Cata WoW is that the writers are agonizing over trying to create impactful factional conflict and introducing new villain tiers for raid bosses. Note how the original three expansions, they were just based around killing established villains built up in Warcraft III.
Once Cata started, they really had to start inventing reasons to kill things, and they already killed all the troll empires off. So they invented new villains, and decided they needed to rile up the playerbase by making suitable targets for destruction.
The only difference between, say, Arthas, and Garrosh, is that Arthas was well written and charismatic. They still did essentially the same things (e.g. Arthas destroyed Lordaeron and Quel’Thalas).
I don’t think Blizz dislikes Orcs or trolls, obviously they love their art design which is why they keep filling up raids and dungeons with them, but your reason for being there in the first place is typically to kill everyone and take all their loot, so they have to be baddies. In order to justify this, you have to give a reason, e.g. OMG they reached out to some ancient evil, we have to stahp them.
That’s why we spent multiple Xpacs conducting troll and orc genocide.
In order to paint Garrosh, and then Sylvanas, with the raid boss brush, they had to do something suitably outrageous to make them godtier villains. And the Night Elves were right there.
Also, Blizz has a history of destroying stuff. Draenor (twice), Stormwind, Lordaeron (twice), Stromgarde, Quel’Thalas, Theramore (actually had to think about the name it was so obliterated), now Teldrassil. Orgrimmar has been successfully besieged and captured once. Very few areas of the map haven’t been pounded into the sand, and very few races are without their utterly catastrophic histories replete with total humiliations.
In a nutshell, no, they don’t hate the trolls, or the night elves, or the orcs, or whomever, they just hate you, the lore-focused player. They love riling you up by dropping badly written lorebombs out of left field to discourage and disrupt you so that they can create more game content.
Blizzard takes an evident and passionate joy from watching you get passionately upset.
As an example, I play an orc. I remember staring wide-eyed at Warcraft II ToD as a child and inquiring “you can play as these guys?” at the goblins and grunts. I remember reading Lord of the Clans and being utterly hyped about Reign of Chaos. I also remember all the batters and dings I sustained to my ego during the last 5 xpacs that we have been raked over the coals and in which all the buildup of the past culminated in the total humiliation and annihilation of our species (which somehow survived and is just fine now for plot reasons). This, too, shall pass. You’ll probably get another world tree in an Xpac or two. It’ll be fine.
Now go kill this boss for shinies, etc.