Simply put, White-The-Fuckery is the nonsense that comes out of many white people's mouths, aka white nonsense. May also be used as white-the-fuck?! To express displeasure at something a white person said.

Briefly, "the realization that each random passerby is living a life as vivid and complex as your own." Originally from the Dictionary of Obscure Sorrows, which has a lot more beautiful neologism definitions like this you might enjoy.