“The last government that took an interest in the racial classification of its citizens ended up eventually sending a few races to the gas chambers.”
Well, no. Other governments since 1945 have taken an interest in citizens' racial or ethnic classification.
Apartheid South Africa was founded in 1948.
State governments in the U.S. still had Jim Crow laws in the 1950s or even 1960s.
Israeli IDs used to state whether a citizen was Jewish, Arab, or Druze. They only stopped that practice in 2005.
I'm sure many Third World governments take an interest in people's race or ethnicity. Or in Africa, tribal identity (a form of ethnicity) might be very important.