You know our government ain't exactly running the table on being able to handle two genders - now you want to give them one, perhaps even more choices. And that doesn't end badly how? Humans rank and count crap. It's one of our most enduring metal problems. And now we have two - one dominant, one not. But you now want a couple more groups to rank higher and lower then the ones we now have. Yikes!
And yes, we have several words that have multiple meanings right off the bat, and moreover are in an area where highly distinct shades of meanings underlay them. You know what? The world is complex and life is so complicated. And even if you get get to this magical place where sex&gender don't matter in a wide number of ways to just about everyone else on the planet, even if you get everyone to agree on one -and one only - highly limited and very specific definition of 'sex' or 'gender', you're still not going to be there because individuals still will see the meanings of the words used, and hence the entire definition, differently.