So far we have gotten four allied races, with two additional ones confirmed to be coming in the future (I'd imagine in the expansion proper) and one additional option that has been effectively but almost incontrovertibly confirmed (though not officially announced) thanks to datamining.
So a question arises: What classes can these races play?
Obviously, the four live ones we already know, but let's take a look at the upcoming ones:
Dark Iron Dwarves:
The only class we have confirmed here was one that could be considered controversial: Paladins. There are, of course, Dark Iron paladins in the Blackrock Depths dungeon, but the Dark Irons' reputation for being somewhat unsavory did make that perhaps non-obvious.
Given that Moira's introduction of the Dark Irons into the Alliance way back in Cataclysm meant Dwarf player characters could now be Mages and Warlocks, it seems pretty obvious that Dark Irons ought to have those classes as well.
With Paladins, it also seems likely they'd have the option to be Priests. Rogues, Warriors, and Hunters are also relatively universal class options, and I doubt that you'd have any trouble convincing anyone of those as reasonable class options.
One somewhat outside-the-box option that Blizzard says they're considering is Death Knights - Dark Irons were certainly around to be turned into Death Knights, and so it wouldn't be so odd to see this as an option - which I'm pretty happy about given that DKs haven't gotten new playable races since Cataclysm.
Shaman I think is a possibility, but unlikely. While the Dark Irons did have a strong connection to Ragnaros, their use of his power was more in the arcane manner - Fire Mages and Destruction Warlocks. The dwarves with a real shamanistic tradition are the Wildhammers.
Theoretically, Dark Irons would have just as much access to Monk training as their Bronzebeard cousins - the Dark Irons were officially in the Alliance as of Cataclysm, which was before Pandaren went around spreading the tradition.
Druids I think are right out - there's no real Druidic tradition for any Dwarves. Likewise, the only races that can't be Demon Hunters that I could imagine giving them (much as I wish I could have made a Worgen one) would be Orcs, Broken Draenei, or Naga if they ever introduce the latter two as playable - just given the representation among the Illidari.
Zandalari Trolls:
Well, we know that they'll have Druids and Shamans, as we've seen druid forms and shaman totems for them. As usual, I think we can expect Warriors, Hunters, and Rogues as fairly universal classes for them (Rogues seem to be fine for anyone who doesn't have hooves, though if Broken Draenei ever become a thing, they could also be Rogues.)
Priests are, I think, also likely given how Troll culture is very mystical and tied to the gods. Trolls also have a tradition of arcane magic, putting making Mages pretty likely. Warlocks, one might have forgotten, were not actually available to standard Trolls until Cataclysm, but they were brought in I think largely because there wasn't a particularly strong reason not to give them, and I don't think the Zandalari have any specific prohibitions against such things.
The Zandalari were technically around to be attacked by the Scourge, but their presence in Scourge-afflicted areas was minimal, which to me suggests Death Knights are unlikely. When it comes to Monks, I'd actually say that it's also very unlikely given that the Zandalari were ancient enemies of the Pandaren back when they were allied with the Mogu (man, questing in Kun Lai is going to be awkward on my Zandalari character. But I guess Searing Gorge will be for my Dark Iron...)
And of course, there's really no practical way they'd do Demon Hunters.
Paladins would be kind of an interesting choice. I can't recall if any of the Zandalari enemies have been Paladins, but we also don't really know what kind of temple-guard traditions they have. I'd put it at a lower than 50% chance, but not 0.
Mag'har Orcs:
For the most part, I'd say we're going to see the traditional Orc class options (pre Cataclysm,) meaning Warrior, Hunter, Shaman, Rogue... but possibly not Warlock. These guys are Iron Horde orcs, and specifically the ones who did not drink Gul'dan kool-aid. It's likely Grommash will be their leader, and so I think Fel magic is likely to be considered far too taboo.
But we could see some alternative options. For example, the Shadowmoon clan has a fairly strong Priestly tradition, so we could see Mag'har Priests. Mages are, I think, less likely - one could perhaps argue that the Blackrock clan employs mages, and of course, similar to Troll Warlocks, they might have given Orcs mages just because, well, why not?
Death Knights seem totally unreasonable, given that their timeline wasn't even connected to ours until after the Battle of Light's Hope and their Ner'zhul went down a different evil-magic path (Void instead of Necromancy.)
Demon Hunters, as usual, are out.
Druids are also probably out as there's no real Druidic tradition among Orcs (though I wouldn't mind getting a better sense of their connection to spirits like Lo'gosh, who either is Goldrinn or is an equivalent wolf spirit the Orcs conflate with Goldrinn.)
Theoretically anyone could be trained as a Monk, and the fact that basically all the live allied races can do it suggests that the Pandaren are definitely still spreading the tradition, so maybe that's going to go into the Warrior/Hunter/Rogue category of universality.