So Tauren seem to get along pretty well with everyone tbh, and have a lot in common with the NE, their only real reason to be in the Horde seems to be that they're honour bound to Thrall, and through that the horde.
Same goes for Darkspear. Vol'jin seems to want peace, and the BE being in the horde shows that Elves and Trolls can put thousands of years of warring behind them.
Goblins seem to just be in the horde because Thrall was the first person they came across, when their slavers ship they were being carried in was sunk (though a lot of that story is a bit daft so we'll ignore it anyway).
BE have shown that they're not entirely against being with the Alliance (until Jaina interfeered) and probably wouldn't mind being neutral at least.
I guess it's just undead that would be screwed.
Seems to me that the majority of the Horde would probably get along fine with most of the Alliance if the Orcs weren't there drumming up war. Most of the races seem to only even be with the Orcs because they were personal friends of Thrall and he happened to be there at the right time to help them. Just saying is all, that maybe Azeroth would all be a much better place if they went back to Outland now their invasion plan didn't work out (if it's stopped crumbling anyway).