This is a question that comes up fairly frequently on this subreddit -- you might be interested in some previous threads that touch on this topic.
"How did Nazis identify who was Jewish or not?" (roundup of past answers by a deleted user)
"Did the Nazis treat Christian Jews differently?" answered by /u/kieslowskifan
"How were Jews identified by Nazis? What happens if a Jew didn't wear the Star of David while walking on the streets in a Nazi-occupied town/city?" answered by /u/ArjanB, /u/Jan_van_Bergen, /u/commiespaceinvader
"Out of curiosity, what would have happened to my family during the Nazi rule?" answered by /u/QuickSpore
"How did the Nazi's know who was Jewish?" answered by /u/shortandfighting