The question seems to stem from the idea that Jews are defined by religion, not by race. Prior to Hitler, such had indeed been the case. In medieval Europe or in Tsarist Russia, a Jew converted to Christianity was no longer considered a Jew. Of course, such a person could be subjected to a more rigorous surveillance than an ordinary Christian (as, for instance, in post-Reconquista Spain) but if the conversion was perceived as genuine, the convert became a full-fledged member of the Christian society. Sometimes such new converts were over-zealous and even became very notorious Anti-Semites.
However, it did not work this way under Adolf Hitler. For the Führer, the race was paramount and the belief was not. The Nuremberg laws enacted in 1935 contained a rigorous explanation who could be considered a Jew.
A person with three or four Jewish grandparents was deemed a Jew. A person with one or two Jewish grandparents was considered a Mischling (half-breed). Whether a Mischling was a Jew or not was determined by his or her behaviour. Marrying a Jew, being friends with Jews or showing any displeasure with the government made the person a Jew. Conversely, marrying a non-Jew and being very loyal to the government reduced the risks. Field Marshal Erhard Milch, commander of the Luftwaffe, was famously a half-Jew (but not necessarily a Jew according to the Nuremberg laws).
In Germany, it was very difficult, if not impossible, to hide one’s Jewishness. The bureaucracy was powerful and the statistics almost perfect. A government official knew who your grandparents were and if three of them were Jews, your only hope was to escape the country as soon as possible. It could be different in other countries, where the bureaucracy was often less efficient and Nazis faced many different hurdles, such as quiet sabotage from the local civil or church authorities. They would often just ask Jews to come forward (and many did!) and then rely on local informants and physical characteristics such as circumcision. It should be taken into account that the scenario could be different in various occupied countries. In France, Nazis, while arresting Jews, often gave them the benefit of the doubt because they did not want to arrest a non-Jewish French person. In Poland or Russia, they were much less scrupulous.
That’s why I will tell a story that happened in France, where it was much easier for a Jewish person to survive. It comes from The Bag of Marbles, an autobiographical novel written by Joseph Joffo.
When Nazis occupied Paris and ordered all Jews to wear a yellow star to make them easy to identify, a Jewish barber gathered his family together and told them that the only chance of survival was to separate, to go to another part of the country, and to conceal their identity. Remember - he told them - never tell anyone you are a Jew. Never. To anyone. Whether you trust this person or not.
Joseph, aged 10, went to Southern France, at first with his older brother Maurice (aged 12), then on his own. He survived by living in various places and doing all sorts of jobs - and never mentioning he was a Jew. He was circumcised, something he could not hide from doctors, so he pretended he had a phimosis. One of the doctors was very inquisitive. Now, it is absurd. So many boys in France pretend they had phimosis. Tell me the truth. I am your friend. I will not denounce you. But no matter how the doctor insisted, Joseph never gave in. He wanted to, but he remembered the words of his father.
In 1944, Joseph, now aged 14, was living on a farm where he was doing field work for his landlord. The farmer, a Nazi sympathiser, never suspected Joseph was a Jew. Every evening he would tell him how Jews were responsible for all the evils in the world and if they kill half of the Jews, the other half will hopefully understand something. Sometimes Joseph started to ask himself whether he was really evil just because he was a Jew. The things were even more complicated for the teen because he was hopelessly in love with the landlord’s daughter.
But when the Germans retreated, the village was occupied by the French partisans. They asked the locals who was the main Nazi in the village and, being told about Joseph’s landlord, promptly built a gibbet to hang him. It was then that Joseph came forward and said: I am a Jew! This man pretended to be a Nazi sympathizer because he was hiding me!
The farmer was released. And Joseph Joffo says he saved him neither out of nobility of character nor out of love for his daughter. I just wished this man to know, until the very end of his life, that he is alive only because a Jew saved his hide.