Ji Firepaw is a monk.
Aysa Cloudsinger is a monk
Arguably Master Shang Xi was a monk
Most pandaren artwork features monks
Taran Zhu is a monk
Chen Stormstout is a Brewmaster, which overlaps with monks.
90% of non-civilian pandaren npcs in Pandaria are monks.
What I am trying to get at is that monks overshadow all other classes in pandaren lore. Blizzard kind of went overboard with the whole kung fu panda theme, even if Pandaren came out before KFP they have been certainly influenced by it (a little too much). Surely there has to be some non-monk Pandaren out there in lore? It is awfully lonely leveling up a non monk pandaren, and I'm sure my character is experiencing an identity crisis =P.
So, where do non monks fit in within pandaren society? There is no mention of the arcane or light in Pandaria concerning pandaren, and the way I see it warriors and rogues are non existant compared to monks. They are even lacking in shaman! I feel like all the fighters the pandaren have are monks, which is kind of rediculous imo.