Could you please elaborate on what you mean by Equal access to rights and resources? The title and the article apart from this one single sentence talk about a matriarchy defined as focusing on collective well-being, empathy etc. and discouraging money and power distribution only through rough, never-ending and non-inclusive competition. So in the context of this article, I read the "equal access to rights and resources" as a blind access to rights and resources without considering differences between human beings. I'll provide some examples from my understanding, so please feel free to ignore reading the following before you respond to this, if you do.

E.g., not considering women, for their biological build-up only, need period and pregnancy paid leaves and care, but instead asking women to leave the paid workforce or suck it up and not demand these "special treatment". I have seen so many men and women justifying that as equal treatment, but it's not. Or, another example would be the gendered bringing up of girls and boys in our society pushing girls to put family and everyone's wellbeing before their own wellbeing or their own wants and wishes in lives and teaching boys the very weird thing of always put their career first, and teaching them if they don't make money or don't financially support the family, people won't consider them as real men which push men to often do as much paid work as they can and put the unpaid domestic care, child and elderly-care load on women and women also often think that is the only right way and police women (and men) who try to walk a different way. So many people justify these things as our "national biological tendency" and justify gender wage gap, men and women's economic and power gap as a result of a fair competition and system, but it's not. Another example will be how we cultivate domineering, unempathetic, violent and might-is-right type persona in our boys and we define those as leadership qualities, and as we shame, police and punish women who lean even slightly towards these very characteristics and also we cultivate completely opposite qualities in women since childhood, many of us think women are not suited for leadership roles, and we call it as equal treatment, but it's not.

I interpret that sentence of yours in this way. So that "equal" is not really an "equal" access, it's a very biased access.
But I am eager to know, what you really meant by the sentence.