Many anti-semitical jokes are not even cracked out of true anti-semitical sentiment. They are only taken that way, because they seem that way. Even when cracked by Nazi soldiers.
Please note that the Nazi soldiers were not per definition bad people. They merely fought "for king and country" like the soldiers of other nations did. Most of them couldn't care less about Hitler. And Germans are humans too. They too were quite often horrified by the things they saw during the war, and humor has always been a way to let things go. To give it a place. This is by the also the reason why tons of jokes about COVID-19 circle around today. When a giant fireworks manufacturer exploded in the Dutch city of Enschede destroying many houses and lives in the process, jokes about the even also circled around for the same reason. Many jokes cracked by the soldiers themselves may just be meant to get things loose... to prevent making the situation get the best of them. Please note that these soldiers were as much under oppression as their enemies. These soldiers would risk not only their own lives, but those of their families and loved ones as well if they didn't bring Jews to the destruction camps. It's hard to sort out who was really fighting for Hitler's ideals and who was not.
Jokes has served many purposes, and yes, unfortunately also propaganda. The problem is that people always assume the worst about a joke. Many jokes even got the joker in trouble due to a group taking offense against whom the joke was not even targeted at all, or to put it even better who were taken in defense by the joker. Loads of problems, jokes included, became big issues, only because people made them big issues.
Learning to take a joke also means to distinguish a joke from actual propagandistic statements or even just blunt insults. Load of people lack that ability. But that is not the joker's fault.