Do you really care about people who will only accept you if you only have a label? I think gen Z cares to much about finding "your people". You know who your people are? People who accept you because you are you, not because you're a X, Y, or Z.
Why would you give a damn about the opinion of someone who only accepts you because you label yourself as whatever? That's a shitty person.
Edit: actually, thinking a bit more about this, that could be pretty lonely depending on your circumstances, because most people are absolute shitbags. So I can understand the appeal of being able to say "I IDENTIFY AS FKLDS;AME" and finding a ready-made community of FKLDS;AME to act as a societal support, since the cishet society you happen to be born into hates anyone who isn't cishet.
Still far from ideal.
I think my privilege is not so much my own cishet identity but simply a geographic one: no one here gives a damn what you identify as, all are equally valid. You don't need to find a new community of FKLDS;AME people or FKLDS;AME allies. Everyone is just groovy about whatever. Less pressure to label.