I am also concerned about some recent social movements in Western countries. They can be seen as reactions to the displacements caused by information technologies and economic globalization. This is somewhat reminiscent, although much milder for now, of the social and political turmoil partly traceable to the effects of the industrial revolution at the end of 19th - early 20th century. At the time the social crisis was accompanied by crises in mathematics, physics, biology, psychology, and yes, philosophy. One of its hallmarks was the rejection of the Cartesian picture of man reduced to his intellect and attached to senses. The backlash against rationalist neglect of other dimensions of human existence was expressed by life philosophy and existentialism (among others), Nietzsche's and Heidegger's, respectively, in particular. But I would not overestimate the effects of psycho-social causation from philosophy to political movements.
One could perhaps say that some philosophies resonated with anti-rationalism and irrationalism, which appeal to the darker sides of human nature. Cassirer, one of the most prominent neo-Kantians, in The Myth of the State names Heidegger and Oswald Spengler (the author of The Decline of the West, and Nietzsche's heir apparent in Germany) as philosophers that "did enfeeble and slowly undermine the forces that could have resisted the modern political myths". But such ideological connections are ambiguous and tenuous. There were Christian existentialists like Marcel and Jaspers, and Dilthey and Bergson were also life philosophers. The architects of red terror chose to appropriate the hyperrationalist Hegelian dialectic instead, and to claim the scientific mantle for Marx's utopian "scientific communism". Lenin made himself into a philosopher because he was dissatisfied with available flavors of Russian Marxism, like Plehanov's. It seems that appeals to intellectual hubris are as capable of servicing justifications for mountains of corpses as appeals to irrational urges. The voices of reason and moderation were also available at the time, Husserl, Freud, the Vienna circle, to name a few, but they just were not listened to by the "masses", and it is doubtful that was due to philosophical rationales.
So we can not draw direct logical connections between philosophical systems and pernicious ideologies. Perhaps, some are more susceptible to the abuse than others, perhaps not. One can see how Nietzsche's will to power, master morality, the Übermensch, and certain "juicy" passages could be appropriated, e.g. this one from Genealogy of Morals:
"In Latin malus... could indicate the vulgar man as the dark one, especially as the black-haired one, as the pre-Aryan dweller of the Italian soil which distinguished itself most clearly through his colour from the blonds who became their masters, namely the Aryan conquering race".
But the big difference between Nietzsche and Heidegger is that the former was simply appropriated, while the latter enthusiastically did his very own self-appropriation with his own two hands. Friedman describes it as a part of interesting analysis of the general philosophical context of 1920-30s in Parting of the Ways (the title refers to the analytic/continental split after 1930s):
"When Hitler came to power in 1933, Heidegger was appointed rector at Freiburg, officially joined the Nazi party, and greeted the victory of the new political movement with his notorious rectoral address, "The Self-Assertion of the German University" [Heidegger, 1933], in May of that year. Although Heidegger left the rectorship after ten months, and in fact appears to have grown increasingly disenchanted with the Nazi regime, he was nonetheless still able, in his well-known lectures, Introduction to Metaphysics, presented in 1935 and published in 1953, to depict Germany as the West's last best hope for salvation from Russian communism on the one side and American technological democracy on the other, and to speak in ringing and famous words, of "the inner truth and greatness" of the National Socialist movement."
Heidegger connected this "inner truth and greatness" to the existential rootedness of authentic Dasein in the "soil", the German soil that is, and grand rejection of inferior "calculating intelligence" in a 1955 essay Gelassenheit ("releasement", translated as Discourse on Thinking). He dismissed new developments in mathematics, science and technology as obscuring the Being and philosophically irrelevant already in Sein und Zeit (Being and Time, 1927), and decried "degeneration of logic into logistic" in the early 1930s. But again, Friedman warns against identifying philosophy with politics:
"Some "scientific" philosophers were and are conservative and even reactionary in their politics... An important example of the former type of philosopher is Gottlob Frege, who espoused strongly anti-democratic, and even anti-Semitic, political views in the period of the Weimar Republic. He shared some of these opinions with his friend Bruno Bauch, who became a leader of "Nazi philosophy" during the National Socialist period (next to Bauch, Heidegger's own involvement with Nazism somewhat pales). Important examples of "progressive" (or at least left-wing) students and followers of Heidegger, of course, are Herbert Marcuse, Hannah Arendt, and Jean-Paul Sartre."