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The point is to put into place systems that will protect you from abuses no matter who comes into power. Those systems, and how well they function, can act as a bellwether indicating how tyrannical the authorities are becoming. If you're lucky exposed weaknesses in those systems can be patched up, and corrupt individuals ousted to shore up your freedoms before things slip too far, but if nothing else those early warning signs can tell you when it's time to get out while you still can.

At the point where you've already been taken over by the new "Nazis" it doesn't much matter. They'll put into place the systems you fear anyway. You say the French today don't keep official records on people's race or religious affiliations, but corporations do, and so that data on the population already exists and could be obtained very quickly. The nice French government today won't touch that data, but New Hitler would.

In the meantime, because France doesn't want to consider race in statistics, it's made documenting, understanding, and addressing the massive racial discrimination problems they have very difficult. For years there have been calls for the French government to start collecting ethnicity data in their statistics because blinding yourself to problems means you can't solve them. (https://repository.uclawsf.edu/hastings_international_compar...) The policy to avoid that kind of data collection was well-meaning, but it turns out that not collecting that data doesn't adequately protect the people of France, and in fact it's actually hurting them.