Podrías usar esta simple prueba:
WHERE (requires = 'privacy-weight' AND privacy-weight = 0) OR requires <> 'privacy-weight' OR requires IS NULL
La primera parte (requires = 'privacy-weight' AND privacy-weight = 0) impide la salida de:
privacy-weight | requires
-------------------------
1 | privacy-weight
Pero mantiene:
privacy-weight | requires
-------------------------
0 | privacy-weight
Mientras que la segunda parte OR requires <> 'privacy-weight' OR requires IS NULL mantendrá los siguientes:
privacy-weight | requires
-------------------------
0 | NULL
1 | NULL
1 | NULL
