Blood Elves: Blood Elves were part of the Alliance (Basically Humans, Dwarves and Gnomes) during the third war, and they fought the scourge together, along with the Orcs (including Trolls and Tauren in the Orc forces), and the Night Elves.
The Blood Elves (formerly High Elves) taught the rest of the Alliance how to wield more powerful magics to take on their foes. Without the race that went on to be Blood Elves there would be
no Alliance mages or warlocks. Jaina Proudmore studied with the High Elves.
After the Sunwell was destroyed (getting no support from the rest of the Alliance) The High Elves became a broken race and became Blood Elves,
still part of the Alliance.
Eventually this desperate but proud race were tricked into facing a situation which would have sealed their extinction by the human Grand Marshal Garithos, forcing the Blood Elves to accept help from the Naga, or die to Garithos' betrayal. How's that for "being part of a group who can actually get along and help eachother"?
With Kael'thas in Outland the Blood Elves entered the horde pact out of desperation because the Alliance used them and left them to die.
Call it convenience, but all the juicy Horde lore is about survival in the face of the fascist imperialism of the Alliance.
Forsaken: Sworn to avenge themselves against the tyranny of The Scourge. Fighting a common enemy can make allies in the most unlikely circumstances (see: all of WCIII). They are consumed with the desire to destroy the Scourge at any cost, and they understand that some "innocents" will die in the process. Again, being taken in by the Horde in their hour of need. Lets face it, if the Horde were really the bad guys, Thrall would be weilding Frostmourne instead of an ex-human.
Orcs: Noble shamanistic warriors that value a good death over cowardice. There is unrest in the Orcish Horde as Garrosh Hellscream is taking the horde to a more barbaric place with every victory in Northrend. This suggest to me that they have a conscience, and values beyond pure bloodlust, even if Garrosh is being a bit heavy handed for the likes of the rest of the Orcs.
Trolls: Night Elves came from Trolls. True story.
Tauren: Just look at them. We don't see them eyeing up the Alliance thinking, "By the Earthmother! I wish we were on the good guys' side".
Speak for yourself!
And: False. See above.
If you haven't played Warcraft 3 at least, I urge you to, if you want to understand your faction.
There are a number of horde quests in WoW which also illuminate various plot arcs and lore which alliance players will miss out on.
I know the opposite is true for players that have only played horde but Blizzard has designed the quests for all players to feel like the good guys, regardless of faction.
In the "spolier" video the Foresaken were there to kill Arthas, like the Orcs and Humans, but they actually looked to do the better job with their new plague.
Fighting a common enemy, with some casualties along the way is a persistent theme in the Warcraft Universe. Remember the battle for mount Hyjal in WCIII? Night Elves, Orcs, Humans and High Elves fighting together on the same side.
There was peace in Azeroth briefly after that, until... the humans started burning Orc settlements, and thus generating more conflict.
/facepalm
Take the lore blinkers off. Many people have been coerced into doing things because "the good cause" is indoctrinated.
I will make no reference to persuasive real world examples as I think the subtext is obvious. And Blizzard do take inspiration from the real world after all.