My personal opinions on what should be changeable:
Cosmetics - Definitely
Class - Yes
First level skill choices even if you stay the same Class - Yes
Stats - Yes, but only to a limited degree, say being able to subtract up to 8 points and redistributing them, to keep more in line with "import" a character
Voice Package - Of course, with some more variety this time around if possible. In PoE 1 I find a somewhat fitting one, but not exactly what I imagined. Side-note: How often voice responses to clicks and similiar things are made would be nice to adjust in a slider or something similar. I grew a bit tired of the feedback towards the end of the game from every click, especially while just exploring. Background, assuming it is even still in game - No, you got beat down, but Eothas didn't time travel and make you change your life choices
Subculture - No, just weird Race - No
Sex - No
Name - No, we didn't lose our memory.
Additional: Factions you've associated yourself with - No Any notable monsters you've killed or allies lost - no