Orcs: Yeah, sure. They’re the origin and backbone. They -are- the Horde.
Trolls: I think in the post-Thrall Horde, they should have very little loyalty to the Horde, but they’d probably remain for the security despite being treated as bottom-rung members most of the time. They’re a small tribe after all.
Undead: I think, logically, Sylvanas would stick with the Horde purely to prevent some sort of witch hunt on her and her people by both factions. However, the story direction lately clearly paints the entire race as comically evil, and I’m sure if it wasn’t for gameplay mechanics, they’d be treated as their own Hostile faction.
Tauren: They were loyal to the Horde because Thrall saved them initially. Thrall is gone. Their loyalty should have left with him. The Horde since then has made too many calls that the Tauren would never make on their own. Too much moral conflict, and I don’t think they need the Horde to survive. They’d be a Neutral faction.
Blood Elves: They have almost joined the Alliance on 2 separate occasions, at least, and share basically nothing in common with the main Horde races. It feels like only their location ties them to the Horde due to the Undead existing. I know why they initially joined, but if we assume the Undead are now their own Hostile faction anyway, I think it makes the most sense for Blood Elves to move on from the past and work with the Alliance, even if they aren’t in perfect sync.
Goblins: They’re literally motivated by money and nothing else. The Horde is currently a vehicle for pure profit for them, so they’re Horde. If Alliance gave them the means of earning similar amounts of gold, they’d be Alliance. I feel like these guys are Neutral almost by definition, even if their morals would align more closely with the Horde.
TL;DR:
Orcs = Horde
Trolls = Horde, mostly for security
Undead = Hostile faction
Tauren = Neutral faction
Goblins = Neutral faction
Blood Elves = Neutral faction or Alliance
Meanwhile, the Alliance all mostly share the same morals at the very least, even if they wouldn’t always make the same decisions. There’s no reason for significant internal conflict in the Alliance, whereas the Horde has constant issue in this regard because their races have fundamental and significant cultural differences.
I feel like if Blizz wantde to sell the Horde races as -needing- to stick together despite their differences, they would have had to have sold the Alliance as MUCH more of an aggressor than they have in all of WoW.