Question is not intended as insensitive AT ALL, it's just genuine curiosity. I'm sorry if it offends anyone, but that is really not my intention.
I think you might be misunderstanding what it means to be Jewish. Jewishness is not just a religion but a cultural and ethnic label as well. A person with Jewish ancestry may be a practitioner of a different religion, but they're still ethnically (and possibly culturally) Jewish and can choose to identify as such. Similarly, converts are religiously Jewish, but that doesn't make them ethnically Jewish.
The Nazis understood it this way as well. Their ideology wasn't from a religious perspective; it was about racial superiority and to them the Jews were a weaker race. The religious practice of any individual Jewish person was irrelevant if the ethnicity/culture were there, so hiding their religion or converting wouldn't have been any protection as long as a record of their Jewish ancestry existed.
Hope this helps!
Hi, you may be interested in a few earlier threads on this subject
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? featuring /u/commiespaceinvader
How did Nazis identify who was Jewish or not? links to several posts collected by /u/OldWorldGlory
The Nazis didn't give the option to survive based on religious conversion. (This was one of the "innovations" compared to the middle ages where one could convert versus modern eliminationist anti-semitism.)
Faking their religion just wasn't a realistic option for the vast majority. It's difficult to completely hide one's identity in peace time; imagine how challenging it would have been in antisemitic Europe during wartime. Lots of things could give them away, from having a Jewish-sounding last name, having dark features, being on a list, having an accent, being circumcised, carrying non-fake ID, etc.
That said, one of my Jewish grandmothers (and her sister too) of blessed memory, pretended they were Polish Catholics to survive the war. (How they survived was so interesting that I am considering creating some kind of film or website about it.) There are a more details that I'm not going to get into right now, but her story seems to be a rare exception due to a combination of courage, luck, physical appearance, and resourcefulness. Even when factoring in all those elements together it was still statistically improbable for her to survive due to the ruthless efficiency of ghetto liquidation, which leads to the conclusion that it was not a viable strategy for the masses who didn't even have her advantages.