Formal equality in its modern democratic/capitalist form is preceded by sorts of political homogenization that existed within the feudal ‘gemeinschaft’, but the latter is an outgrowth of natural alienation and reflects a partial decomposition of communal norms, while the former demands the total reconstruction of basic social ties in the terms of capital. In the feudal context, a contradiction develops between the individual and society which does not exist in 'primitive communism', and in these limited communities ‘the political’ becomes the domain where individuals affirm their ties to one another through systems of reciprocal obligation & subordination to the rituals, traditions, and mythos that emerge to ensure that they endure in the face of the harsh realities of the natural world.
It is in this cleavage of the community into a mass of interdependent individuals, who are assorted into caste-like orders (or 'estates') which perform a variety of social functions - (i.e. in the further development of alienation) - that the interlocking bases of commercial development, democracy, and (eventually) capitalism are nestled. As is argued in Yorks article, ancient democracy can be directly linked to the sorts of social differentiation & commodity exchange that existed within Greece, despite how primitive they were.
So while it would be wrong to say that there's a direct or transhistorical identity between democracy and capitalism, as doing so would mean making the ridiculous suggestion that e.g. Ancient Greece was already capitalist, and that's not the claim that marxists make (or need to make) here. What we do claim (and what is indisputable) is that there's a homology between the logic of capital and the logic of democracy, and that the growth of the former streamlines and reinforces the latter in a way that has no true parallel within pre-capitalist societies, nor under communism:
”The democratic phenomenon appears with clarity in two historical periods: at the time of the dissolution of the primitive community in Greece; and at the time of the dissolution of feudal society in western Europe. It is incontestable, that during this second period the phenomenon appeared with greater intensity, because men had really been reduced to the status of individuals and the ancient social relations could no longer unite them. The bourgeois revolution always appears as the setting in motion of the masses. From which arises the bourgeois problem : how to unify them and fix them within new social forms. Hence, the institutional mania and the outburst of right in bourgeois society. The bourgeois revolution is a social revolution with a political soul.
During the communist revolution, the masses will have already been organised by capitalist society. They will not seek new forms of organization but will structure a new collective being, the human community. This appears clearly when the class acts in time as an historical being, when it constitutes itself as party.”
- Jacques Camatte, The Democratic Mystification