Communists agree, and this is why democratic Socialistts such as Oscar Wilde praised the fact that Communism nurtures individualism, especially for those in the arts and sciences. He wrote about this in The Soul of Man Under Socialism:

"What is needed is Individualism. If the Socialism is Authoritarian; if there are Governments armed with economic power as they are now with political power; if, in a word, we are to have Industrial Tyrannies, then the last state of man will be worse than the first. At present, in consequence of the existence of private property, a great many people are enabled to develop a certain very limited amount of Individualism. They are either under no necessity to work for their living, or are enabled to choose the sphere of activity that is really congenial to them, and gives them pleasure. These are the poets, the philosophers, the men of science, the men of culture – in a word, the real men, the men who have realised themselves, and in whom all Humanity gains a partial realisation. Upon the other hand, there are a great many people who, having no private property of their own, and being always on the brink of sheer starvation, are compelled to do the work of beasts of burden, to do work that is quite uncongenial to them, and to which they are forced by the peremptory, unreasonable, degrading Tyranny of want."

Your idea that anarcho-capitalism is a legitimate heir of the liberal ideas which were used to found the US is, to be honest, a silly one - as one can see the exact opposite in the writings of the Communists and anarchists whose whole idea was based on the freedom of individuals and their free association, something which even individualist anarchists such as Stirner realised is not possible with private property.