the actual criticism by those on the left is that private ownership of the means of production necessitates an inequitable heirarchical relationship between an ownership class and the working class.
this relationship is enforced by the state, which is essentially an abstraction of capital, by inflicting violence in order to protect the interest of the capital owning class.
neoliberalism is conservative in that it functions to conserve this status quo, offering incremental material improvement as a social pressure-release valve, but liberal democracy can not deliver liberation to the working class because of its primary function of enforcing private capital.
most liberals don’t consider neoliberalism conservative because the coloqial usage in US contemporary politics is referring to the reactionary position of the christo-fascist right.
counterpoint;
eat my entire ass, red fash.