The whole right wing/left wing thing as they are used in our political speech, for Libs on one side and Conservatives on the other, is really just wildly inapplicable to the Nazis. To top off that shit sundae of bad thinking, and to use a favorite DU-ism of days gone by, the DUmmies are always 'Conflating' political philosophies (Like monarchy, dictatorship, oligarchy, or democracy) with economic systems (Capitalism, Socialism, and Communism). Any of the one may be paired with any of the other...Nazi Germany was a dictatorship politically but a limited form of Socialism economically; Red China is an oligarchy but far more Capitalist than Communist these days, though for a fair time it was indeed a dictatorship and Communist.
And by the way, YellowRubberDuckie, you won't find it much discussed on the History Channel since it doesn't play into the agendas of the producers who pay for and make the programs there, but the thing that started Germany spiralling out of control after the Abdication was uppity Reds declaring Soicialist paradises in places like Munich. This was immediately followed by them proceeding to kill anyone who wasn't on board for it. Order of a sort was eventually restored after a year of virtually-unreported civil warfare by the Freikorps, but the Reds weren't crushed, just deposed.
The ensuing thirteen years or so saw two economic crashes, one caused by crushing reparations and the next caused by the global economic collapse triggered by US protective tariffs which were reciprocated against US goods by all the other manufacturing nations that we screwed. The Communists and trade unionists were very willing to do violence and anyone who wanted to stand against them became equally violent in response or quickly learned to shut up (If they still could), so street warfare was a constant. Into all this mix on both sides were millions of demobilized Soldiers who had endured possibly the most Hellish war of all time, and to many of whom any human life besides their own meant damned near nothing at all.
It took that kind of society to put a Hitler in power, and he was welcomed because when he came to power, he actually was an honest-to-God improvement, unless you were Jewish, though that wasn't such an obvious issue at the start, and only became clear once he had uncontestable power and it was too late to unpeel the apple. Structural issues with the Weimar political system let him grab power as he did in a young and poorly-established state, all of which are totally alien to the US system of government.
So if you're so concerned about it happening here, always stand up for Constitutional government, fight to break the political power of trade unions, and bitchslap a Commie.