I'm going to go by a mix of what I'd like to see, and what wouldn't require too much independent focus. In short, races that could either piggyback off of this expansion and its themes for lore, or could be partnered with another race and effectively share bases and lore with it. For example, Draenei/Lightforged Draenei can be paired together quite easily, sharing bases, story, and so on. I doubt anyone would complain if those two usually showed up together. Same with Dwarves and Dark Irons, who are now allied. Or Tauren and Highmountain. Nightborne and Blood Elves have a similar enough magic focused culture that no one would waste a second glance if they were almost always working together. Zandalari are probably going to tie into Troll lore in general and will probably get more development than the Darkspear ever did.
Main point here, partnering races up makes it easier to make lore for them, rather than splitting the focus a thousand different ways. The more allied races you add, the more you're going to want them partnered into shared chunks for more convenient lore and story development. Nightborne and Blood Elves, and their story, are likely going to be deeply involved with one another in the future.
That way, it's less likely for them to be completely forgotten expansions later and less effort would need to go into giving them development specific only to them, which would save a hell of a lot of time in the long run. Void Elves are the only exception, but we look to be headed towards lots of Void development in general. So that fits into piggybacking off the expansion.
Horde:
Non-green Orcs: Exactly what it says. Whether they be brown or some shade of grey, or even red, the basic culture would still be an excellent fit with their Azerothian brothers. Even if we got some former Iron Horde Orcs working alongside us, bringing their more distinctive technological aesthetic as well, I feel that'd only enhance and broaden their shared Orcishness rather than conflict with it. If they were all working together, I doubt anyone would complain that their favorite color of Orc wasn't getting enough independent attention.
Other Trolls: Pretty much the same deal, though admittedly trickier, an option opened up by the inclusion of the Zandalari. While different Troll cultures are indeed different, they wouldn't exactly look out of place working side by side if the Zandalari approved it. The Horde already has the Revantusk Tribe. Troll fans would likely appreciate Troll lore from any tribe, and relish a chance to not have to slaughter them all. I doubt even the most hardcore Darkspear fan would mind it too much if Troll bases and towns got a little more diverse. Hell, I think they'd mostly just love Trolls getting continued attention and lore. However, this will likely be the end of any truly independent Darkspear development. As if there had ever truly been much to begin with.
Taunka/Yaungol(Other Tauren): Taunka already joined the Horde. While culturally and physically more distinct from standard Tauren the Highmountain seem to be, they could still easily be lumped together in many cases or fill a similar role to what Tauren generally fill. Maybe not so gentle, bu they'd still fit as a variant. Yaungol would be harder, and they'd likely have to play up how different they and their culture are, but perhaps that could be part of the "Tauren" story in general. This would definitely broaden the themes and attitudes associated with Tauren, meaning more distinct character archetypes available for Horde bull-people, but likely also open up rifts and internal conflicts. It'd be something comparable to the cultural incongruities between the different Dwarven Clans.
Undead Elves: Humans aren't the only race the Scourge raised in mass, and I'm pretty sure a significant portion of Forsaken are already supposed to be Elves. Not just the Dark Rangers, either. There are references to Sylvanas's Royal Guard being predominately Elvish in origin. They're theoretically already part of the population. Including them would mostly just broaden the Forsaken, rather than distract.
Leper Gnome: Maybe you could also shove in Leper Gnomes, since a lot of them like to hang out with the Forsaken and they could get along without stepping on the other's toes. I don't think it'd be too troubling to make them a more regular feature in Forsaken outposts, whereas Goblins would be more associated with the Western Horde.
Alliance:
Wildhammer: Already technically part of the Alliance. Wildhammer Dwarves pretty much are already part of the main Dwarf storyline and development, and have been for awhile now. In a sense, they represent something I've already mentioned above. While culturally distinct from other Dwarves they're compatible enough that it really just broadens and adds onto the Dwarven race as a whole. As such, they're an ideal candidate for a fairly low effort Allied race. Already got plenty of lore ingame and are already fairly well partnered up with regular Dwarves and the Alliance as a whole.
Frostborn: I honestly don't know much about them, but nothing I see shows them as being incompatible with Dwarves in general. They're already part of the Alliance and led by a Bronzebeard. Including them would not be much of a challenge, even if they didn't have as long a history with the other Dwarven races or are biologically a little more unique. They even have decent candidates for racial mounts. They're an easier inclusion than Nightborne, if they ever feel like revisiting Northrend.
Broken Draenei: A better option than Lightforged Draenei if you ask me. Lighforged seem to me to just be regular Draenei, but moreso. However, that works if they're mostly going to be sharing lore and development. However, Broken Draenei are also already a part of Draenei culture these days. Maybe they have a different attitude than most handsome Draenei, actually having Rogues and such, but they could be included in the same settlements. Whether they be from Argus, Outland, or both, they're an excellent candidate for an allied race that broadens the themes of its host race. That's already part of the themes of its host race and already has its main Shaman characters. It'd be nice to have them as the somewhat shadier underbelly of Draenei culture, especially since they're masters of stealth while regular Draenei can't even be Rogues.
Vrykul: No. These would work better as an independent race. They don't tie in especially well with the focus points of this expansion, and they don't work too well as partners for another race. I already consider the Yaungol a stretch. Vrykul are also a bit too big. A somewhat smaller Vrykul-like race could work, but they'd have to give them a lot of attention this expansion. If Kul Tiras humans/Drust end up having some more primal/Vrykul-esque traits in their culture and physiology, that's probably the closest we'll get to Vrykul. And it will probably be done in a way that allows them to connect to general human culture. Hopefully without erasing their identity entirely. Something that might give us more insight into how Humans lived before they became generic Medieval Light-worshipers, and so expand our understanding of standard Human history as well.
Elf Worgen: Human Worgen also developed something of a relationship with Night Elves, and Night Elf Worgen already exist. It honestly would not be difficult to make a story for recruiting some ancient Druids of the Pack from the old days, and they could easily fit with both Worgen and Night Elf stories. If you wanted to put real effort into it, you could make their Worgen forms more slender and tall, give them longer ears, and maybe colors more reminiscent of Night Elf skin and hair colors. Not too difficult to implement.
Furbolg: Honestly, these should probably be their own race. They aren't even culturally similar to Pandaren, and would likely be more aligned with Night Elves. So really, they shouldn't be on this list at all, except for the vague idea that Allied Races are likely to be variants of pre-existing ones. But I think Furbolg should be added anyhow, if only to help give Night Elves some allies more traditional allies to associate with independent of the Eastern Alliance or the Tauren. Night Elf fans always seem to complain that the Alliance has been consuming their identity, and the only thing I can think of to reverse that is to have Night Elves associate more with races that could balance out the Human influence. Something to help keep them grounded to their more savage, in-tune with nature, Kalimdor side. Something to give them a set of allies and partners with an identity separate from the mainstream Alliance.
Other than that? Who knows. That's all I feel like I can asspull at the moment. All of which I think could potentially fit in as a sort of partner to a preexisting race, something that could complement or expand their lore even if it creates some cultural conflicts. Furbolg thrown in as more of a reach, just because I really feel the Night Elves need allies that help them look like something other than a purple twist of generic fantasy human-ally-elves. That kind of reduction will keep happening so long as developers don't feel Night Elves are even a little out of place standing side by side with humans.