I remember in elementary school (and beyond) hearing teachers point out the following problem with Christianity: If a Nazi believed in that religion then he would automatically be saved despite his sins. Not so in Judaism, where a person must be punished for his sins. As I grew older, I realized that this is not an accurate representation of either Christianity or Judaism. Regarding the latter, the question remains whether a nazi who repented his sins would be forgiven. While there is no real need to try to be God's accountant, I believe that there is merit in exploring this area of theology for the theoretical sake. On that note, I believe that this issue is a matter of debate between the Rambam and R. Yosef Albo.
The Rambam (Mishneh Torah, Hilkhos Teshuvah 6:3) writes (link):
It is possible to commit a great sin or a number of sins... which hinder repentance and do not allow one to return from one's wickedness, so one will therefore die and be destroyed because of one's sin.This is how the Rambam explains God's hardening Pharaoh's heart. Because Pharaoh had already sinned so terribly, God prevented him from repenting. Similarly, Elisha ben Avuyah-Acher heard a heavenly announcement that he should not repent (Chagigah 15a). One can plausibly suggest that Nazis also reached this status where God does not allow them to repent.
R. Yosef Albo (Sefer Ha-Ikkarim 4:25) disagrees with this position and argues that God always leaves open the door for repentance. Every human being, while still alive, retains the ability to repent. However, generally God assists those who try to repent because it is very difficult for a person to do this without help. Those who have sinned greatly will not receive that assistance. But they can still repent if they are able to achieve it on their own. (Many other voices have added to this discussion and I am just presenting the two main views.)
Thus, one could suggest that according to the Rambam a Nazi would not be allowed to repent while according to R. Yosef Albo he could but would not receive divine assistance in the matter. One could point out that while repentance is conceivable for many sins, when dealing with the atrocious interpersonal sins of the Nazis, repentance is impossible. How can millions of dead people forgive them for their misdeeds? While this logic is compelling, I believe that the Gemara does not accept it. Regarding the Babylonian general Nevuzaradan, who killed thousands of innocent people, the Gemara (Gittin 57b) states that he repented and converted to Judaism. If he, murderer of so many innocent people, could repent, why not a Nazi? While the Rambam might say that he did not reach the state wherein God prevent one from repenting, the fact still remains that a mass murderer was allowed to repent. Clearly, interpersonal sins does not prevent repentance. (Unless one wants to suggest that conversion would neutralize the sins but not repentance alone.)
In his discussion of the Gemara regarding Nevuzaradan, R. Joseph B. Soloveitchik discusses the possibility of repentance for Nazis (The Lord is Righteous in All His Ways, p. 274):
Teshuvah helps, even for Amalek. I have often wondered whether if a Goering, a Goebbels, or a Hitler, yemah shemam ve-zikhram, may their names and memories be blotted out, showed signs of sincere penitence and was ready to change into a decent person, would we accept him? I have no answer. There is no doubt that no matter how cruel the murderer Nebuzaradan was, the Nazi gang was worse. Clearly Nebuzaradan was superior to Eichmann and to Hitler. I believe that the Nazi gang personified the most corrupt, the cruelest, and the most arrogant leaders or tyrants who ever existed in the history of humanity. But yet, the Rambam writes that "Nothing can stand in the way of teshuvah" (Hilhot Teshuvah 3:14).I am not sure why he does not quote the Rambam I cited above.
The verse says about Manasseh, "Moreover, Manasseh shed much innocent blood" (II Kings 21:16). And Hazal tell us that when Manasseh was taken captive, he was subjected to torture and began to pray to the Almighty; he was ready to repent... But Manasseh, a king of the Jews, cannot be compared with the Nazi gang. Although he was a wicked man, he was a thousand times above them.