The fundamentals of political ideology are really pretty simple.
People on the right care more about natural order and hierarchies, so whoever has a position of power due to tradition (conservative), supposed superior skills (liberal), gender or race (facist) deserves to have more power. Inequality is naturalized.
People on the left are for a more egalitarian, democratic society. As Faust has pointed out, this include non-government spheres like workplace democracy. I am no Marxist but I respect Richard Wolff, a Marxist economist, for always pointing out how crazy it is that we accept authoritarian workplaces. We dont even consider the alternative to our Western system of representatives who are not bound by the will of the represented, namely council delegates who are bound.
I life in a country where proclaiming that Φcalan (the guy who founded a political ideology that led to the currently arguably most democratic political entity in the world, Rojava) is a decent guy is considered to be an act of terrorism.
In other words, anarcho-capitalism wears the veil of formal democracy, considers this to be end of history, ignores the actual increase of inequality of wealth and power and clouds the actual paths towards a more democratic life.