1. They should deliberately introduce noise into the raw data. Nazis with the raw census data can spend all month trying to find the two 40-something Jews that data says live on this island of 8400 people, but they were just noise. Or were they? No way to know.
2. Bucket everything and discard all raw data immediately. This hampers future analysis, so the buckets must be chosen carefully, but it is often enough for real statistical work, and often you could just collect data again later if you realise you needed different buckets.
3. They shouldn't collect _anything_ personally identifiable. Hard because this could be almost anything at all. If you're 180cm tall your height doesn't seem personally identifiable, but ask Sun Mingming. If you own a Honda Civic then model of car doesn't seem personally identifiable but ask somebody in a Rolls Royce Wraith Luminary...
The antidote of oppression is not the Index statisticum prohibitorum, but quite the opposite, education, and in particular educating about how different each and every one of us is, and yet it doesn't take much to get along well.
(Or, of course, simply pass a law that entitles them to deport or hold indefinitely anyone who can't prove they're a real Ayrian with only the papers they have on them at the time)
Remember; fascists don't believe in things because they are true, but because they are a means to an end. Their ultimate goal is authoritarian control, and an administrative mechanism is far more effective toward that goal than a scientific one.