Where's the conflict between Marx and Nietzsche?

Twilight of the Idols, Expeditions of an Untimely Man, S34, Hollingdale translation

Nietzsche says here "anarchist" and also "socialist" because basically all anarchists at that time were socialists. Hopefully this passage sheds some light on your question.

Christian and anarchist. - When the anarchist, as the mouth-piece of declining strata of society, demands with righteous indignation 'his rights', 'justice', 'equal rights', he is only acting under the influence of his want of culture, which prevents his understanding why he is really suffering - in what respect he is impoverished, in life. . . . A cause-creating drive is powerful within him: someone must be to blame for his feeling vile. . . . His 'righteous indignation' itself already does him good; every poor devil finds pleasure in scolding - it gives him a little of the intoxication of power. Even complaining and wailing can give life a charm for the sake of which one endures it: there is a small dose of revenge in every complaint, one reproaches those who are different for one's feeling vile, sometimes even with one's being vile, as if they had perpetrated an injustice or possessed an impermissible privilege. 'If I am canaille, you ought to be so too': on the basis of this logic one makes revolutions. - Complaining is never of any use: it comes from weakness. Whether one attributes one's feeling vile to others or to oneself - the Socialist does the former, the Christian for example the latter - makes no essential difference. What is common to both, and unworthy in both, is that someone has to be to blame for the fact that one suffers - in short, that the sufferer prescribes for himself the honey of revenge as a medicine for his suffering. The objectives of this thirst for revenge as a thirst for pleasure vary according to circumstances: the sufferer finds occasions everywhere for cooling his petty revengefulness - if he is a Christian, to say it again, he finds them in himself. . . . The Christian and the anarchist - both are decadents. - And when the Christian condemns, calumniates and befouls the 'world', he does so from the same instinct from which the Socialist worker condemns, calumniates and befouls society: even the 'Last Judgment' is still the sweet consolation of revenge - the revolution, such as the Socialist worker too anticipates, only conceived as somewhat more distant. . . . Even the 'Beyond' - why a Beyond if not as a means of befouling the Here-and-Now?. . . .

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