“Nietzsche was unequivocal about his hostility to socialism, a leveling ideology, he argued”

https://jacobin.com/2024/08/nietzsche-marx-fascism-felsch-review

Beyond being a “leveling” ideology the problem that Nietzsche objected to was its tendency to be a homogenizing ideology.

Industrial-scale capitalism within the context of globalized mass society is bound to produce an egregious extent of inequality. The communitarian scale and ethos of bioregionalism tends to work against inequality. But it also tends to work in favor of diversity. Socialists have a tendency to want the world — all of it — to look a certain way (the way they have in mind). Nietzsche abhorred the social engineering aspect of the movement. He found universalism unnatural and pathological. He felt our civilization leads in that direction and he hated it.

In our time Nietzsche might have been a featured writer for the journal Green Anarchism.