When I say liberal values are the ‘basis’ of Marx’s work, I am not suggesting he was a ‘liberal reformer.’ I am arguing that Marx’s work is a dialectical sublation of liberalism. He takes the some of the liberal achievements (rationalism, the end of feudal bondage, and the Labor Theory of Value) and shows that they can only be fully realized by moving beyond the capitalist mode of production. He doesn’t reject the ‘Individual’ out of hand; he rejects the liberal version of the individual (the abstract citizen) to make way for the real individual (the species-being).
Only when the real, individual man re-absorbs in himself the abstract citizen, and as an individual human being has become a species-being in his everyday life, in his particular work, and in his particular situation, only when man has recognized and organized his “own powers” as social powers, and, consequently, no longer separates social power from himself in the shape of political power, only then will human emancipation have been accomplished.
– On The Jewish Question




I agree that the liberal state is a tool for class power and that formal equality is often just a mask for material exploitation.
When I say liberalism is the basis of Marx’s work, I am referring to its humanist core: the promise of individual autonomy and self-determination. With the exception of private property, the values you listed contain a seed of humanism that is currently restricted to a select few.
Nothing forces a value like autonomy to be contingent on private property. Marx shows that private property is exactly what prevents autonomy for the majority. By explaining why these values fail under capitalism, Marx is not dismissing them. He identifies the property relations that prevent human progress. He argues that to actually realize the individual rights liberalism promises, we must first abolish the class power used to protect them for the few.
Even more so, Marx took a core liberal value, the free development of the individual, and proved it is materially impossible to achieve under a system of private property. He analyzed liberalism by holding it to its own standards, showing that the very system it created could never fulfill the values it proclaimed. This is why I call it incomplete because it offers the legal form of freedom without the material content.
Marxism does not do away with the individual. It identifies the material conditions, the abolition of class, required for the individual to be truly autonomous. Marx does not throw away the promise of the Enlightenment. He offers the only material path to make it a reality for everyone.
P.S. I think treating liberal idealism and Marxist materialism as mutually exclusive is a bit non-dialectical. Liberalism was a material response to feudalism, not just a daydream. Likewise, Marx did not start from zero with a cold science of factories. He took the enlightenment goal of human dignity and used a materialist method to discover why that goal was being strangled. To Marx, ideas are themselves a material force once they have gripped the masses and formed a collective consciousness. To suggest Marx had no guiding ideas is just as one-sided as suggesting that liberal thinkers were fully divorced from the material world.