1 - Which Faction should they join?
The Horde. According to Chronicle, the Horde allied itself with the Magram Centaur back in Vanilla. Now that the Centaur Clans of Desolace are united, if they had to join one side, I feel like the Magram would tip the Centaurs towards the Horde.
Also: Let’s not forget Dorthar, the Horde Centaur.
2 - But don’t the Tauren hate them?
The Tauren are a forgiving and understanding people, especially now that they kicked 3/4 of the Grimtotem out.
In fact, the Horde is the forgiving and understanding faction. The Elves of Quel’thalas, the Orcs that invaded Quel’thalas and the Humans of Lordaeron who imprisoned the Orcs in internment camps all fight and drink together now.
Besides, the Centaur who would join the Horde are not the bad ones from the Barrens, but the relatively good ones from Desolace.
3 - Why though?
Because I like Centaurs.
4 - Which Classes should they have?
Priests, Rogues, Druids, Hunters, Shamans and Warriors.
5 - Wait, what? Druids?
The Centaur of Desolace revere Cenarius.
6 - What about Mounts?
They could have a Racial to use Druidic Shapeshifting Magics to transform their horsebits into humanoidbits. Have that Racial automatically turn on when they mount and automatically turn off when they dismount / enter combat. All is well.
7 - What about Leg armor?
Just do the same thing Blizzards does for Tauren / Draenei, but twice.
8 - Why not Dryads instead?
9 - Would you accept X Race as a compromise?
Neigh.