There were "moderate" Nazis in OTL. A Goering or Speer in charge of things post-Hitler would be very different than a Himmler or Heydrich post-Hitler. There were many Germans and even Nazis who were anti-semites, but who would never had initiated the mass murder of them. If Hitler dropped dead anytime between 1936-1941, it's highly unlikely any Final Solution is ever approved by Kanzler Goering. The Nuremberg Laws and occasional pogroms were enough to satisfy all but the most ardent anti-Semites.
The level of mass murder done under Stalin, Hitler, and Mao can only be done for a certain period of time. Sporadic pogroms are one thing. Ongoing, systematic bloodshed another. Most people (not everyone - sadists are out there and definitely occupy a high place in the Nazi party) will eventually recoil. Once the prime architects of these horrors go away (whether by purges or natural deaths), it is more likely than not that the deliberate mass murder stops. Of course, another reason it'll decline and stop is that the initial purges will eliminate a lot of "reasons" for its support to begin with. Germany itself won't have any Jews, Gypsies, or Slavs, and for most Germans, that'll be enough. Support for ongoing systematic murder further east is going to drop, especially once resistance intensifies as urban, middle class professionals refuse to become farmers in Ukraine. "Why kill the remaining slavs when we need them to farm the land and give us grain," will be mentioned.
When things do "moderate", it depends on who is in charge. If a Goering or Speer takes over, it could happen as early as the fifties. If Himmler or Heydrich, then maybe not until the 1970s. A lot will depend on what happens to the SS and whether they are able to take over the state. They will be the ones driving an eliminationist agenda. The rest of the party not so much.
Doesn't mean the moderate Nazis wouldn't be evil, but we're talking the difference between Brezhnev and Stalin.