I think the problem is deeper than Gender to an extent, I think ultimately it's tied into the "tribe/team" mentality. We feel a need as people to create teams and groups, then define ourselves based on rival teams and groups. And Boy-Girl is simply one of the oldest examples. Which is why I think society and people have a hard time accepting people who aren't "team players"
I don't know if the Binary should go away completely either, It's natural for there to exist duel concepts, and ultimately it's through the differences of cultural concepts that we define ourselves (I mean if male and female didn't exist as two things we would probably get some bland in-between, as oppose to a dynamic in-between created through molding two forces).
But I do agree that it needs to be chipped down to be less of a overwhelming force. I honestly don't know how to fix it, to me it seems like an ingrained human trait, which is passed down by parents who really only know how to teach manners through a spectrum of what is or isn't acceptable (and part of that is their concepts of gender norms).
I think it's like asking to get rid of hate, bullying, and discriminating. It comes down to needing a fundamental change in everyone which is too much to ask of such a diverse world of goods and bads.
There are ways to chip at it I guess, moving to a gender neutral bathroom system might help, getting rid of the gender question on forums that don't need it, time...
It makes me think, and I hope that one day we can at least get closer to a world that is less ready to define people as abnormal for how they feel I guess...
