If being a believer of the Judaism religion, it would not be of surprise that there would be some that would abondon their believes in order to sustain their life in such a harsh time. Was this possible? If so, how popular was it?
No, this would not help, especially in Nazi Germany, and generally in conquered areas although it seems like there were more gray areas there.
I'm sure more can be said, especially about some of the gray areas, but u/kieslowskifan has a good summary here:
To nazis, "Jews" were a race, and having Jewish ancestry made you part of that race (the specifics are in the handy but disturbing charts they include in their answer).
If a Jewish person successfully evaded detection they would have pretended to be a different religion as just one part of a more all-encompassing disguise.