My head canon says
"Wuteng" for the people, as in, "I think the Wuteng are very handsome."
"Wuteng or Wutain" as an adjective, "Wutain food is my favourite."
"Wute" if you want to be offensive and racist. "Hey, slanty-eyed Wute bastard!"
The insult used in game for them is "Wutai flea". Actually not in game per se; I think it's used in "On the Way to a Smile: Case of Yuffie."
Not I think my head canon is always right or anything.
Kassi, this talk of a Rude fic intrigues me muchly.