Oz and NZ definitely no issue. I stayed in some pretty small motels in some pretty small towns in NZ and not even a raised eyebrow (not sure if small towns in Oz are the same but the cities are definitely fine).

Tahiti is also fine as is Rarotonga (Cook Is). You'll find gay staff in most resorts and Fa'afafine's are well known and accepted in both countries. I've certainly never encountered any negative reactions and I'm sure you'd enjoy both places.