The "shame" that Arnold refers to is really a post-war development. As Omer Bartov shows in his painfully expensive The Eastern Front, 1941-1945: German Troops and the Barbarization of Warfare, the average soldier was given quite a good indoctrination into specifically why and for what the war was being waged over. It wasn't as though these motives were hidden from them in the least; officers were instructed in giving pro-Nazi lectures, for example. Anti-Semitic and anti-Bolshevik literature was widely disseminated.

This kind of indoctrination was fairly common throughout all armed services. Charles Thomas' The German Navy in the Nazi Era gives a good account of how this played out in the Kriegsmarine, and Herbert Warner's Iron Coffins, while fairly problematic as a historical source, at least provides some post-war reflection on how this was accomplished.

The alleged shame is really a function of two things: trying to not be arrested and tried as a war criminal and trying to distance oneself from the Nazi apparatus as best you can. Doenitz and Raeder's respective memoirs avow that they were never Nazis, they were vigorously against the persecution of the Jews, and they only felt shame at what happened. Maybe after the war, yes. Similarly, Von Manstein's memoirs try to portray the Wehrmacht Heer as an apolitical fighting force that took no role in Nazi atrocities. Again, this is completely belied by the historical record.

/u/psstein and /u/flobota have already made very good points already. What I can additionally weigh in with, is this older answer of mine discussing the level of knowledge among Wehrmacht soldiers and how the Wehrmacht as an institution was crucially involved in war crimes. I draw heavily on books discussing the Allied protocols of recorded conversations between Wehrmacht POWs that show that during the war, knowledge of the Holocaust and war crimes was wide-spread and common and that one of the greatest fears these people expressed was Soviet/Allied victory for fear of being treated the way that they had treated their victims.

What bears pointing out is that from these sources, historian Felix Römer worked out that there was violence regarded as legitimate, e.g. against Partisans and people who were perceived as such, and violence that was seen in a more critical light by members of the Wehrmacht. Take this exchange between soldier Friedrich Held and Obergefreiter Walter Langfeld about the topic of anti-Partisan warfare:

H: Against Partisans, it is different. There, you look front and get shot in the back and then you turn around and get shot from the side. There simply is no Front.

L: Yes, that's terrible. [...] But we did give them hell ["Wir haben sie ganz schön zur Sau gemacht"],

H: Yeah, but we didn't get any. At most, we got their collaborators, the real Partisans, they shot themselves before they were captures. The collaborators, those we interrogated.

L: But they too didn't get away alive.

H: Naturally. And when they captured one of ours, they killed him too.

L: You can't expect anything different. It's the usual [Wurscht ist Wurscht]

H: But they were no soldiers but civilians.

L: They fought for their homeland.

H: But they were so deceitful...

[Römer, p. 424]

While this on the whole shows that violence against civilians was rationalized as a necessity of anti-Partisan warfare, it does offer a glimpse into an understanding that it is not always the case that they targeted the right people. It is not wholly unlikely that views such as this transformed into shame and guilt post-war.

However, it is not really possible to say how widespread this phenomenon was because we lack significant scholarship on the subject, most likely to do with an absence of sources.

What we can further expand on is how German and Austrian post-war society decided to engage with the topic and while from a political perspective the Federal German Government pushed heavily for the "Clean Wehrmacht Myth" exonerating Wehrmacht soldiers of their responsibility, there is an ambivalent social tendency in that these societies at large developed the strong tendency to make the war and the crimes committed during it forgotten and keep it out of public debate.

To use an example that encapsulates this: The first chairman of the newly founded Social Democratic Party in Germany was Kurt Schuhmacher, a staunch anti-Nazi who had survived the camps and lost his arm in the process. Several historians of post-war Germany have pointed to the fact that his not being successful as in not becoming chancellor in the post-war era was related to the public perception of not wanting to have a top tier politician who so visibly had the traces of Nazi crimes inscribed in his body. Basically, Schuhmacher lacking an arm, hampered his party's chances in elections. It is the same tendency that inspired one of the earliest historians of the Holocaust, survivor Joseph Wulf, to write to his son: "Ich habe hier 18 Bücher über das Dritte Reich veröffentlicht, und das alles hatte keine Wirkung. Du kannst Dich bei den Deutschen totdokumentieren, es kann in Bonn die demokratischste Regierung sein - die Massenmörder gehen frei herum, haben ihr Häuschen und züchten Blumen." (I have published 18 books on the Third Reich and it had not impact whatsoever. You can document yourself to death with the Germans, there can be the most democratic government ever in Bonn – the mass murderers are free, have their houses, and raise flowers)

And while this, as Wulf expresses, lead to a distinct lack of public engagement with Nazi crimes and criminals, at least until the first Auschwitz trial in Frankfurt, it also resulted in an ambivalent attitude towards Wehrmacht veterans in Germany. They did receive their pension etc. but public displays of honoring veterans so familiar to some socialized in the US I presume were not really in the cards in post-war Germany. Veteran organizations had this shadow existence where some of them had hardly any impact at all, while others – like the Kameradschaft 4 for Waffen-SS veterans in Austria – became hotbeds of Nazi activity post-war.

Where I am trying to go with this is that the lack of public interest at large displayed for veterans and the world of veteran organizations, at least for the people involved in that, could also make an impact on this idea of shame and/or guilt. The problem, again, is that however present shame and guilt was, there was preciously little public display of that with those returning from the war. My guess is that Arnold is basing that off of his private experience and this most likely shaped a lot of the post-war family life in many cases but it finding little entrance in public discourse makes it hard for historians to get into that.

If that assertion necessarily holds up there is, in my opinion, not necessarily the most important element because whether the individual felt shame, Arnold's point that everything that came in contact with Nazism was in some way affected by it horribly holds up. Germans and Austrians who had a hand in these crimes and in some cases instigated them really did live for the longest time as members of these new societies, having their houses and raising their flowers. The murders and criminals were integral part of German and Austrian societies in a myriad of ways, like being integral to forming institutions like the German FBI equivalent BKA, continuing to work as doctors like Heinrich Gross, working for the government like Globke, and even forming their own political parties with some times barely veiled Nazi members like the FPÖ in Austria.

The presence of these people combined with the fact of the societies of both Germanies and Austria through the realities of the Cold War and other factors dealt with this past, the way it did, which is to say, in many ways insufficiently, has resulted in some cases in grave injustices. Not just in people like Nazi doctor Heinrich Gross being able to treat some of his former victims again in post-war times but also in e.g. a much too late compensation for former forced laborers taken from their home and forced to work for the German war machine (done in 1999 and 2000 respectively), a much too late amnesty for Wehrmacht soldiers who deserted (2002 in Germany, 2009 in Austria), insufficient restitution of property and so much more.

Personally, while things have changed in the meantime, I sometimes can empathize very much with the sentiment Jospeh Wulf expressed above because while today, the mass murders have mostly died peacefully in their sleep, the struggle with their criminal legacy and the insufficient response of post-war societies is still one that is present.

I think Arnold's statement paints in the usual broad brush strokes which are problematic when talking about this topic. Of course he might have well met some former Nazis that were ashamed. But let's look at two points in that question which make it hard to answer very easily:

What is a Nazi? Are we talking about members of the Nazi party? Are we talking about every German that had some part in the Third Reich? Are we just talking about the soldiers and politicians? Depending on how you define the group you are talking about you will get increasingly complex results here. I think the term "the Nazis" is too broad to debate something as individual as shame.

Shame for what? Don't get this question wrong, I just want to point out that men like Klaus Barbie who, like many other former nazi functionaries, continued living in South America or Rudolf Hess, who hanged himself 30 years ago in Berlin-Spandau prison, might have felt no shame at all. Or if they were ashamed that it was more about losing the war than what they actually did in the war.

Moritz Hoffmann points out in his book "Als der Krieg nach Hause kam" that especially younger people that didn't know much else than the Third Reich were shocked when the war was over. So, these youngsters might have felt shame for losing as well. Or later on as /u/psstein points out because of the social context that came to the conclusion that their blind following of Adolf Hitler was something shameful. But on the other hand, in the same age group you have people like Helmut Schmidt, later German chancellor, or Günther Grass, later German Nobel price winner who were rather belonging to the so called Flakhelfer-Generation, they might have been ashamed for actually serving in the war in some sort. But even that is complicated since the Flakhelfers also defended their hometowns for example.

As for the soldiers for example, it gets even more complex, it made a huge difference on which front they served for example or what age they were. Just as a personal example, one of my great grandfather was conscripted when he was 40 and served for one year in Italy before he died there. I have a lot of letters where he goes on and on about how much he hates the war. But that's just one in a few million men. It might have been very different for the guy next to him even.

The last big debate in Germany and Austria about this happened during the Wehrmacht exhibitions in the 90s when more veterans were still alive and generally, the topic could be discussed more openly after the reunification. I think there is a clip on YouTube where a few Austrian veterans visit the exhibition and rant about it and how it portrays the Wehrmacht.

I would like to add to the question: was there a shame gap between the soldiers that followed every order and those who did their part in resistance movements and refused inhumane orders?