Not quite.
The Alliance:
Hates all orcs because of what the ones in the Burning Legion did.
Hates all trolls based on the actions of tribes they'd encountered before the Darkspears.
Hates the Forsaken thanks to the Scarlet Crusade convincing everyone that all undead are evil regardless of who's controlling them, preventing Alliance members from seeing those not under the control of the Lich King as just family members with a tendency to decompose.
Abandoned the High Elves in their time of need. Granted some of them did become corrupted and turn into Naga, and cause the Great Sundering, but then some of the Night Elves succumbed as well, becoming satyrs. No-one started hating on them. Or the Draenei for that matter. They got corrupted too, some becoming Eredar. The Alliance really has some double standards.
Taurens and Goblins, they joined the Horde. That's clearly enough reason to hate them too.
The Horde:
Hates being persecuted.