The nonbinary category, from the beginning, seems to have been proposed as a category of unlimited privileges, even in places with no self-identity. It allows a person to change nothing about the way they look, dress, or act, but still demand access to all sexed spaces.
I have seen transgender organisations state that nonbinary people should be allowed to compete in sports in whichever category they decide to, to use male and female toilets, based on how they feel, to access all single-sex facilities and so on.
I have also noted that certain nonbinary female people are very vocal online about the importance of erasing the word 'women' in all reproductive and other health information, because "they need it, too, and they are not women."
So here inclusiveness seems to expand the rights of one group to break all boundaries while other groups have more limitations put on them (such as women not being allowed to refuse a male person entry to a dressing room, or not being allowed to have a name for their actual biological group).
The gender fluid version suggests that some individuals could have two identity cards, depending on the day and on how they feel that day about their genders etc.
This is interesting because it doesn't come with the same burdens as being transgender (no expectation of bodily changes etc), doesn't reduce the male privilege for any male person (as they can just choose to be taken as men when it suits them), and, perhaps sadly, will not reduce the sex-based discrimination and misuse for nonbinary female people that women will face in most societies (as misogyny won't choose its prey on the basis of pronouns).
It's also interesting when you think of the old argument that third genders have existed in many societies, because in most of them third genders were about gay men, and in almost all of them belonging to the third gender came with many rules and limitations about how the person could otherwise live. The new version is nothing like that.