I'm sorry if this is a bit insensitive and crass, but couldn't they pretend they were Catholic or something?
https://www.reddit.com/r/AskHistorians/comments/2wj741/how_did_nazis_identify_who_was_jewish_or_not/
A little dated now, but a user (who deleted his account so I can't tell who it is) compiled some previous threads on the topic