Clark and Leiter write in Nietzsche: Daybreak, "there is no evidence, however, that Nietzsche ever read Marx". He was aware of socialists and Young Hegelians more broadly, like Strauss, Stirner and Feuerbach, and yes, his individualism and emphasis on the historical role of "exceptional individuals", was antithetical to socialism and historical materialism, and his philosophy of life was antithetical to everything rationalism, especially Hegel.
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The crux of Fukuyama's argument is to examine first the proposition that we may have reached the "end of history" that Hegel talks about, at least in the political sense, and then to relate that proposition to Nietzsche's general aversion to the idea of any sort of "final state." Nietzsche doesn't mention the philosophical term "recognition," but he's talking about many of the same problems that arise from the way human beings place value on events, things, and other people. Fukuyama may not be as averse to "final states" as is FN, but he's extrapolating from what FN wrote to question whether a "final state" of human affairs would be desirable, in the various ways Hegel and Marx present the idea.
Your earlier remark about not needling a universality is key to Nietzsche's take, insofar as he can be said to state, as Fukuyama says he does, that humans need to pay more attention to the quality of recognition, rather than quantity (my rewording).