I don't say that no one's fighting for equity or for equality of outcomes. (Mind you, there's a lot of confusion about what "equity" is supposed to mean.) I say no one's fighting for that in the absolute sense that concerns Rothbard. Even in a fully communistic society, there are dictators who can't be considered equal with the workers. So Rothbard's talking about an extreme that strawmans egalitarianism.
The question for me is what secular humanism is supposed to entail. How do we maximize not just negative but positive freedoms, the freedom to fulfill our potential? Should we allow free competitions to take their natural course, as in anarcho-capitalism, or should we correct society's course when necessary to help the losers get ahead by enhancing their chances? If the government doesn't step in at all to equalize those opportunities by giving the lower class some artificial advantages, you lose social cohesion, which leads ultimately to violent revolution.
It's not so easy in practice to disentangle the equalities of opportunity and outcome.