The reality of this trope is far more complicated than the trope itself.
You might think that eugenics, Social Darwinism, and reverence for the ancient tradition of Jew-bashing would be a perfect match for a system of hereditary privilege, but in practice this trope was often defied in Real Life. Nazism, while anti-democratic and racist, was a strongly egalitarian and meritocratic populist movement when it came to traditional social class lines (among "Aryans", at least), and aristocrats found no special place in Nazism. While the old nobility were not keen on democracy, they were a class of themselves, and usually strongly disdained the "plebeian" Nazi party, whom they often viewed as rabble risen from the gutters. The majority of the 20 June 1944 conspirators to kill Hitler were noblemen. Except for Hermann Göring, all of Hitler's inner-circle Nazis were commoners with little or no distinguished ancestry (Joachim "Von" Ribbentrop cheated by ensuring that he was formally adopted by an aristocratic woman, but he was not a nobleman by birth). For the Nazis' part, the feeling was mutual: many of them held the aristocratic Prussian nobility who lost World War I in nothing but contempt. When the deposed Kaiser Wilhelm II sent a letter to Hitler expressing his hope that the monarchy would be restored, Hitler simply remarked to his valet, "What an idiot!"
With regards to the military proper (as opposed to the SS), it was more sympathetic to the old traditions and had a number of old-style nobility in it who were Just Following Orders. This was a great bother to Adolf Hitler, who couldn't get along without them but absolutely hated officers; partly because he had once been an enlisted man (during World War I more than half of the German officer corps was composed of noblemen), partly because they often had minds of their own within the confines of their profession, and partly because they deflected loyalty away from him.
To start with, Nazism was, from beginning to end, a populist, grassroots movement, and German aristocrats were opposed to the involvement of the common people in politics as a matter of principle. In fact, one of the antisemitic arguments made by the Nazis was that Jews were greedy social climbers. The German and the Austrian professional/upper-middle classes (the highest class of society besides the gentry and the industrialists) had a disproportionally high proportion of Jews, which antisemites tended to exaggerate long before World War I. And not only that, a number of Jews became nobles themselves (more commonly after converting to Christianity) either by receiving a title themselves or by intermarriage. This trend already led many ideologues of a racist (i.e., non-religious) antisemitism before World War I to look on the nobility as "unreliable". The Nazis held mass rallies and recruited ordinary Germans into paramilitary organizations like the SA and the SS; noblemen loathed the idea of mass rallies (or mass-anything, really), and were worried about the fact that the Nazi paramilitary organizations did not recruit their officers from the ranks of the aristocracy, as the German Army had traditionally done. But those noblemen who hated the democratic Weimar Republic, not to mention communists and Jews, with a passion saw the Nazis as useful allies to get rid of them, some — most notoriously Franz von Papen — even deluding themselves that either Hitler would become more "sensible" once he consolidated the new regime or that they would be able to make him do what they wanted. And, of course, the more political power Hitler concentrated in his own hands, the less power was left to go around for everyone else. Nor did the Nazis merely seek to compete for political power, they aspired to replace traditional focuses of loyalty; in effect, Nazis and the aristocracy were competing for the same space and in that sense were adversaries as much as allies.
However, from the end of World War I, Hitler and the Nazis took their cue from the Dolchstosslegende (the legend of the "stab in the back") promulgated by the Field Marshal von Hindenburg and the old army command after the fall of the German Empire. This stated that the German army had not been defeated in the field, but was forced to accept an armistice because the November Revolution of 1918 rendered Germany incapable of continuing the war and ultimately forced it to accept the Treaty of Versailles in 1919. This was, of course, a blatant lie which bore no relation to the hard facts of the situation of Germany and the other Central Powers in 1918, but it was what many Germans desperately wanted to believe. So when Hitler first attempted to seize power in the Beer Hall Putsch of 1923, he did find some support from the old officer class, even though the most prominent co-participant, Erich Ludendorff (formerly Chief of the General Staff and Hindenburg's military "brain"), was in fact a commoner.
So, even though many among the German and Austrian nobility partially or wholly agreed with Nazism's assessment of "lesser races" and were eager to reassert German military strength in Europe, they generally resented Hitler's appeal to the masses and lack of regard for tradition. Some of them also felt that Hitler was incompetent, and that his war strategy was disastrous, and although some aristocrats had low opinions of non-Germans, Nazi racial extermination policies disgusted most of them. Aristocrats were disproportionately involved in military plots against Hitler, but whether this was because of this or simply because aristocrats were disproportionately represented in the officer corps is a matter for debate.
At the same time, Nazis did woo the nobility — with considerable success. Despite his humble origins, Hitler was very adroit at social events and when he wanted to he could display tremendous amounts of charm and etiquette knowledge in posh settings, impressing the upper crust. A more important factor in this was that in 1934, Hitler, Göring, and Himmler suppressed the SA, the militia that Nazis relied heavily early on in their history, the SA high command being summarily murdered in the Night of the Long Knives and the rest of the organization made insignificant. This was because the SA had been deemed too crass and rowdy for the tastes of the upper classes and the churches. For Hitler to gain credibility with the "respectable" classes, the SA had to disappear from sight. The fact that the supreme leader of the SA, Ernst Röhm, and part of his entourage were unabashed homosexuals made the murders of the Night of the Long Knives even more popular in some circles. Many officers and noblemen, even some who would later join the resistance, applauded them and saw them as proof that Hitler was the right man to lead Germany, even though the Nazis had at the same time settled a number of other old scores and also murdered a number of prominent conservative and right-wing politicians and officers, including former chancellor and general Kurt von Schleicher and former Bavarian Generalstaatskommissar Gustav Ritter von Kahr (who had foiled Hitler in 1923). The Reichswehr high command subsequently did not hesitate one moment to order the German armed forces to swear loyalty to Hitler after the death of President Paul von Hindenburg in 1935.
In place of the SA, the SS gained more influence and, specifically, to make it more respectable, Paul Hauser, a highly regarded regular army general, was brought in to organize and train its military branch, the Waffen-SS, with proper military discipline. By 1938, a fifth of all SS officers were noblemen. High-born noble families were particularly prone to Nazism: between one third and one half of all eligible people with princely titles joined the Nazi Party. And, of course, the Nazi Wehrmacht was built out of the earlier German armies, so they inherited all of the officers wholesale, including a bunch of aristocratic officers, natch.
There are many reasons that this trope keeps recurring, but some of the main factors include confusing Imperial Germany with Nazi Germany, simple prejudice against aristocracy in general and specifically against Prussian nobility, a desire to include cool titles and ancestral castles, and assuming that everyone who opposes democracy does so for exactly the same evil reasons (also the reasoning behind Commie Nazis). In part this springs from a desire to keep things simple: to speak of "the aristocracy" and "the Nazis" as quasi-monolithic blocs is already a simplification that glosses over the serious differences within these groups; the differences between different Nazi factions led to the "Night of the Long Knives", after all. The recurrence of the trope often is also related to unfamiliarity with German affairs, for instance the cliché that every German officer is a nobleman (and usually from an old family, not one whose title only dates back a generation or two), which ignores the ever-growing numbers of non-noble officers since The Napoleonic Wars.note Another problem is that superficially, the Nazi ideology of "Racial Superiority" sounds like something that ought to dovetail neatly with aristocratic superiority. Unfortunately, writers who focus too much on "official" Nazi ideology tend to miss the fact that the increased popularity of the Nazi Party was also driven by envy, resentment, and fears of inferiority. At the same time, Himmler did see the endogamous practices of the nobility as a model of eugenics.
The reaction to a trope can become a trope itself. Of course, in many ways Imperial Germany led to Nazi Germany, and the German Army fought a genocidal war of extermination for the Third Reich. Both of these rather obvious points have been deemphasized in — not merely German — public discourse, thanks in part to the early entrance of post-war West Germany into the Western bloc. There, after the war many social and political formations liked to claim that unlike the rest of Germans they had been impervious to the appeal of Nazism. Thus communists said that the "real" working classes opposed the Nazis to a man, Catholics said that Catholics were immune to their seductive powers, and noblemen stressed how much the nobility despised and shunned those "plebeian" brownshirts. Since noblemen still played a big part in post-war West German media and government, that last message was successfully disseminated. As a consequence, for a long time the only anti-Nazi dissidents who received official recognition (and large-scale media recognition) in West Germany were Stauffenberg and his noble co-conspirators, and to a lesser extent some Christian groups, most notably the White Rose. Other resisters tended to be glossed over or dismissed as traitors (especially if they had connections to the Soviet Union, like the "Red Orchestra") or even as Nazi agents provocateurs (this happened in the case of Georg Elser, who came close to killing Hitler on his own with a time bomb on 8 November 1939).
To some extent, this trope also applies to the British nobility. A small number of the British aristocracy were sympathetic to the Nazis. Unfortunately, the handful that were sympathetic were also the ones everyone remembers, often because they were very good at marketing themselves. This means that there are a lot of Britons out there who are wrongly convinced, and often convinced beyond dissuasion, that the aristocrats were all Nazis. Ironically, Winston Churchill was himself the grandson of a duke and a former admirer of Benito Mussolini; numerous other members of Churchill's administration were similarly high-born (although only two or three titled aristocrats were members of Churchill's War Cabinet, many if not most were related to peers in some way—politics being a common pursuit for younger sons of aristocrats). Even among the British aristocrats who did have far-right, quasi-fascist leanings, most were such knee-jerk British jingoists they loathed the Nazis anyway (a prime example being Lord Redesdale, aka David Freeman-Mitford, whom his communist daughter Jessica called "one of nature's fascists" but who only accepted his Nazi daughter Unity's fraternization with Hitler when she persuaded him he was a thorough Anglophile—and promptly went back to hating Germans after the beginning of the war).
