Actually during WW2 , I have read many Jewish holocaust memoirs , where the Jewish rabbi & ( And Jewish Council ) gave permisson for the Jewish adults & children to be put in Catholic covenants under FALSE Christian papers in France , Poland & Italy. Also the JOINT was aware & helped too ! Many different Jewish rabbi's said to preserve the Jewish race from extinction The Jewish people could pretend to be Christians . In some Jewish holocaust memoirs the Jewish person ACTUALLY posed as A Muslim . If you look at SOME Hungary Jewish memoirs you can find the info !!!
Pretending to be someone else, another identity, is not the same as converting. The Nazis were looking at race not religion so Jews were pretending to be racially someone else. The Nazis did not care if someone was a practicing Catholic. If they knew that a parent/s were Jewish they would consider them of Jewish blood. It was a racial not a religious thing.
Also exctinction of Jews was not an issue. European Jews constituted 50% of the world's Jews, a sizeable percentage but not all.
The governing doctrine that conversion is impermissable was set out by Maimonedes (Rambam) in relationship to the persecution of Yemenite Jews by the Muslims.