Well, the core problem is that as long as how someone understand this has an element of subjectivity, you can't define your way of it, because other humans will in effect just think/feel differently.
I get what you are trying to do, but in itself playing definitions won't solve anything.
Humans talk about subjective things all the time, correct?
What is the purpose of this thread? More specifically, what are you hoping to achieve with it?
The scientific and medical definitions for sex, gender, and gender identity are all readily accessible online, so I'm not sure how or why the opinions of laypeople would change much, if anything, regarding said definitions. Are you trying to explore how people's opinions on sex and gender identity might compare to the expert consensus?
What I observe when I see people talking about these topics is - more than usual - people talking past each other or arguing over semantics. The thought was that if we could agree on definitions of terms the conversations would be a lot more productive.