After watching CNN's documentary "The Sixties" I noticed several scenes of young American men (18-25) who were clearly Nazi or sympathetic to their cause (in dress, speech, and action). So the question immediately came to mind: "Why would this specific age group take up the banner of Nazism?" These are members of the generation born right after WW2 - whose parents saw first hand the atrocities of anti Semitism and what it did to our world. Certainly these adults knew this, right.
You have to remember that fascism as a movement is by definition reactionary. Fascism didn't develop in a vacuum, and never would have existed without the Socialist Revolution in Russia, and the radical social changes taking place in Europe in the interwar years. All of the Empires of central and Eastern Europe had collapsed and been replaced by either politically shaky liberal Democracies or by the USSR and her aggressive early attempts to export the revolution to her new neighbors.
Fascism was the polar opposite of this, which formed specifically to prevent the destruction of Europe under the totalitarianism of the Soviet Union. The root of the nationalism inherent in fascism was the rejection of the internationalist message of communism, which saw a strong state as the only bulwark against communist expansion: weak or divided politics or weak economies were ripe for communist insurrection. Nationalism's logical conclusion if taken to the extreme is chauvenist and ultimately racist: eine Reich, eine volk, eine fuhrer. The only way to really create a strong state to resist socialist undermining was to totally unite the people along popular, linguistic and political lines totally subordinate to the state, and the exclusion of all undesirables from public and ultimately private life (the specific designation of these people's is what fluctuates from party to party).
So, in a time of economic or political instability in any metropolitan society, it is easy to use the fears of foreigners or racially diverse citizens as benefitting too much at the expense of the self identified national ideal. If there is a true socialist movement in the world, it is even easier to intellectually justify it extreme nationalism.
The 1960s in the United States met these requirements, so it is unsurprising to find it. Today, however the Soviet Union and international communism are extinct, so the hard right movement is reduced to cruder racism and an ultra nationalism unlikely to really ever become mainstream, much like far right parties in contemporary Europe. Disaffected youth with shaky economic prospects are easy to recruit, and can be a significant danger to society on a small scale, but are unable to translate into real political power in the absence of a serious internationalist movement seeking to overthrow the current world order.