Truthfully i am surprised they can even BE any other class but monk.
Really? How close-minded can you seriously be?
Pandaren still have eat, don't they? Still need clothing? They weren't always able to get all their goods from a farm, y'know, so Hunters make sense. Also, considering how in tune they are with nature and the elements, Shaman fits well. Given the Mogu seem to have some ties to the Titans, Mages make perfect sense as the Titans' meddling has always had a basis in the mystical and the arcane.
And not everyone has the mental discipline to be a monk, but they still have the desire or inclination to be more martial in their life, hence Warriors; flip that coin, even, since not everyone has the martial prowess to be a Warrior or a Monk but still have vast amounts of mental and moral fortitude, so Priests work. And, to step back to Shaman, Pandaren still aren't Priests in the same sense as a Human or a Draenei, but more like a Tauren Paladin, seeing the light as an extension of a different belief system.
It seems to me that, along the lines I've laid out, Pandarens can't be Paladins because being a Paladin requires both great mental strength and a bias towards martial prowess; Monks and Shaman get close to this balance point, but still neither require quite the same commitment or fortitude as does a Paladin.