Jews, Homosexuals, Political dissidents, Gypsies, Slavs, Russian POW's, mentally ill and disabled...all were sent to their deaths in significant numbers.
In Germany in the 1930's, it wasn't a case of proving someone was Jewish, it was a case of them having to prove that they weren't Jewish. For a large section of the population, that meant producing certificates of baptism going back three generations. All over Germany, Churches were inundated with requests to provide certification of baptism/christening, and to their eternal shame, the church leaders obliged.
In the Eastern and Balkan states particularly, the Jews were more Orthodox and much easier to spot from their dress, habits and traditions (Orthodox Jews also lived in other parts of Europe too, such as France). In many cases, families were reported to the authorities if they were known to be Jewish. The Nazis also looked for certain facial features they deemed generic to the Jewish people, and if you fell under suspicion, you had to provide your proof of ancestry.
One of the more disturbing aspects concerning how Jews were gradually rounded up was that in occupied countries, the responsibility to identify and register Jews fell onto local Police forces. As many people were of course completely unaware of the fate that would befall these people, those Police Forces regretfully obliged the ruling Nazi authorities. Even in France and the Channel Islands, this is known to have taken place.