A lot of the OP is drivel about making the Alliance racist or genuflecting to the fact that Horde races are ‘coded’.
You don’t need any of that.
Focus on the fact that the Horde is naturally a bit more liberal and chaotic in regards to their way of life, lean into the fact that their identities are a lot more disparate and unique from one another and turn them into a confederation trying to fulfill those needs while focusing on how their leaders are addressing those needs.
How is the Darkspear Chieftain keeping his people connected to the Loa? How is Lorthemar encouraging the deepening understanding of the Light and the Arcane magics in a way that is beneficial? How is the Forsaken leader helping the undead find purpose and validation and justification to be around? Continue the exploration of Orcs shouldering the burden of carrying their sins.
Orcs built the Horde. The Horde is founded on Orcish ideals. The Trolls had to adopt its ways and leave aside some of its old ways. The Tauren embraced their values because it resonated with theirs and they settled. Either an Orcish Warlord or a council with leaders on equal footing is required to keep this thing afloat.
The Horde should be an entity seeking to better itself through glory in battle, deepen its ties to its mysticism, posture itself toward incremental improvements both martial and academic. In order to grow, it’s going to need capital and economy, and that means competition with others, including the Alliance, but not only them.
The player has the impression the rest of the world is weak, because the character we play grows beyond everything else so quickly. That Centaurs are not a threat, that Quilboars are not dangerous, that the myriad beasts and races and factions in the world are not worthy of the Horde’s attention. The Alliance doesn’t have to be the only enemy worth fighting, worth raiding and plunder, worth the Horde’s endeavors to prove itself in battle.
There should be respect between the Horde and Alliance. Not held hands, not as friends, but to understand that they are dangerous to one another, and fights that erupt between them will be deadly. Neither the Horde or Alliance should always be instigators or defenders, but slant the Horde toward being reactionary. Defensive. A constant middle finger presented to the rest of the world in warning that they will not be trifled with, but if interfered with, will leave nothing but rubble in its wake.
“If they do not give us peace, we will give them war.”
Something will push up against the Horde’s borders before long, and it doesn’t need to be just the Alliance, either. If it does, there’s no need to make a competition of resource something as grand as the literal blood of Azeroth. Stone, lumber, farmland, and much more mundane things are always going to be needed.
In contrast, let the Alliance play as its opposite: Rigid, orderly, conservative and stagnant. They do not have or need a diversity of faiths, cultures, or opinions because most of them abide by what is largely the same sets of culture. Humans, Gnomes and Dwarves are practically homogenous in their faith systems, with Gilnean Worgen and Kul Tirans only marginally different. The Harvest Witch renaissance and Tidesages of Kul Tiran faith systems do not contrast greatly with the overarching values in the way the the Horde is splintered in their more vastly different styles of mysticism.
Imbue the Alliance with what they consider the moral justification to impose itself upon the Horde. Play up the fact that the Alliance sees the Horde as monsters, brutes, shambling corpses and beasts.
Fundamentally, it’s just doubling down on how they’re already presented, putting down the splintered villain bat and being less afraid to tarnish the Alliance. Beyond that, just make the world show a bit more teeth so that whenever we don’t have a world ending threat like the Scourge or the Legion that the world still feels dangerous and that the Alliance and Horde are fighting it to stay alive-- and that it sometimes means fighting each other.