Historically "identity" wasn't a right, but something imposed on people, for better tracking and controlling them by authorities...
>In an oppressive state identity surely could be oppression, just like everything else, but in a democratic country?
Oppression is not about democratic vs totalitarian state. McCarthy and Hoover, to mention just two examples, reigned over others in the good ole democratic US of A.
Not to mention very few (if any) countries have actual direct democracy, or give the people say in how they want to be governed, from the constitution and downwards.