The Catholic Church often gets slammed for not speaking out against Nazism during World War II. History is never as black and white as popular cultures likes to think. The Catholic Church did try to stay neutral during World War II. The Vatican was surrounded by Nazi allies and to choose sides would have made it a target. There was three options that the Church had. The Church could, 1. Choose sides and speak out against Nazism and be shut down and likely sent to concentration camps. 2. Take an official stance of neutrality but work behind the seen to help the Jews. 3. Do nothing and risk nothing.
So what would have happened if the Church would have taken option # 1 and publicly condemning Nazism? I don’t know if it would have saved a lot of Jews. The Vatican spoke out against the current American war in Iraq and this did not seem to impede the war. I find it unlikely that the Nazi’s would have shut down the furnaces of Auschwitz because the Catholic church condemned what they were doing. I do believe that this is the position that Christ himself would have chosen though. This would have been a hard cross to bare when it’s your own women and children being lead to the concentration camps. (3000 Catholic Priest were killed by the Nazis) If I was Pope during that time, and I’m glad I’m not, I don’t know if I could have chosen this hard road. I don’t think I would have the strength.
I believe that option # 2 is what the Catholic Church did. If you look for where the Catholic Church acted to try to help the Jews you will find some really admirable acts by the Catholic Church. (see this Jewish perspective) If your question is where did the Catholic Church failed to act, you will find plenty as well (another Jewish perspective).
If you look at option #3 it is really hard to say that this is what the Catholic Church did. The truth is that the Catholic did act and it did take risks to help the Jews although it could have acted more. Popular culture likes to believe that the Catholic Church did not act at all and this is simply untrue (as the first link above shows)