It really depends on the fan. Most people are okay with people of any race, ethnicity, skin colour yadda yadda cosplaying since it is after all, just playing. I'm sure there are some out there who get all bent outta shape that a white gal wants to dress up as Korra, but they're getting mad about nothing.
Do keep in mind that when it comes something like, oh I dunno, the casting for a major motion picture based on the series, Asian and Native (Inuit or Yupik, for example) actors should be cast in these roles. It is a pan-Asian fantasy world, after all.