One distinction to keep in mind is the difference between equality of means, and equality of products (what one makes, or can make of one's means).
Enforcing the latter is the false friend of liberal democracy, reducing everyone to the lowest common denominator, and absorbing them into a herd so gigantic that they lose the power to influence anything, for the benefit of the few elites who run the milk factory.
On the other hand, inequality of means is how the whole postmodern stealth oligarchy is able to retain a tremendously powerful social caste system while increasingly destroying all of its formal signs, which are more vulnerable to criticism and inspiring revolt (e.g. racism? discrimination against gay and trans people? Nah, look at Obama! Look, gay marriage! Never mind all those imprisoned, homeless, enslaved, constantly fearful and structurally murdered people that make up a much larger segment of the population). Instead, we have statistical systems that ensure most people of a given group never escape massive exploitation, while a few do so that they can be used to control the others and fondle the middle class with their myth of heroic progress.
Equality of means just means that everyone starts out with fairly equal access to resources and time, as much as possible, and some naturally do more with them than others, and that's fine, so long as they aren't oppressing the others, and everyone joins hands to make sure they don't if they try it, hopefully! (combining with the anarchist anti-hierarchical idea). Something like this really is necessary to prevent a stealth hierarchy. You can't just give one person good food, lots of free time, a family with free time, a safe neighborhood, and lots of books, and then give another person no free time, malnutrition from lack of enough food, few books that can help, two jobs on top of schoolwork, a terrible, mandatory 'educating' system, and constant presence of police and other violent thugs who are there because of gov. policy, and expect the two people to have an equal chance. Ending that system is a radical demand.
Of course, the legal equality people are either building treadmills for others or running on them themselves. The existence of a hierarchical state precludes by definition any idea of actual equality, even under the law, since, ya know, some people run that thing, and some other people don't. Hmm. I wonder who made that thing and why, way back when. Funny little contraption, it is. People still believe that court building claptrap their whole lives though, even if it doesn't make sense on closer observation.