Ich would translate that by
Kategorie.
Zustand suggests a time dependency, Status would work, but is somewhat blurry, State has far too many meanings and would require a concise definition.
Alternatively a compound could be used, as e. g.
Kundenstatus
To reflect the somewhat shifted focus in the edited question: Here also the following can be considered:
- Attribut(e), which would also correspond to class attribute
- Eigenschaft(en)