Setting aside the obvious fact that Marxists have almost universally been responsible for some of the biggest failures in attempting to liberate people from capitalism (to be fair, anarchists have also not fared much better), which is a historical a posteriori problem and thus doesn't interest me: It should be assumed that anarchists are not very much in favor of Marx, considering that anarchists aren't Marxists.
There seems to be some misconceptions some people have that anarchists and Marxists are essentially the same, except on the question of the State. If this were true, libertarian Marxists like the Situationists and Autonomists would basically be anarchists, or vice versa anarchists are basically libertarian Marxists, right? But there is a distinct difference between even anarchists and libertarian Marxists: Anarchists by and large don't use Marx as the basis for their ideas. There is certainly something to be said for Marx's critique of capitalism - however painstakingly lengthy and repetitive it is - but one could likewise argue that Marx's critique of capital is both superfluous up to a certain point and also only touches on the problem of capitalism. Marxists tend to subordinate (starting with Engels) any questions of the State under dialectical materialism; they tend to assume that the dissolution of capital will just magically fix every other issue, because they make the a priori argument that everything can be rooted in the material conditions of society. And this is where I take the biggest issue with Marx and Marxists.
Certainly the material conditions of society are a major factor in how power is distributed in society. I don't think any anarchists are opposed to this idea. But to argue that everything can be traced to material economic conditions just blatantly ignores the plasticity of human beings. The material conditions of one society may affect it differently than another, because the culture of that society and the psychology of individuals in that society also affects its conditions. It seems to me rather that Marx and Marxists seek to essentially reproduce Enlightenment narratives of human rationality by supposing that we will more or less react equally to any given material economic conditions. Marx and Engels sought to give their ideas the character of a "science", to make objective claims to "truth", and anyone who ever claims that they have "solved" things and have know the "truth" because of their one weird trick are not to be trusted, IMO. It's a classic reactionary move to claim that your position is the rational, logic, and truthful one - and even if you believe this, you unknowingly carry a whole host of meta-assumptions in your position. It's no surprise then that Marxists have had to gradually allow for Marxism to deal with racial and feminist struggles and not simply write them off for being the "superstructure" and thus subordinated to class.
To put it another way: It's not the material conditions that entirely determine how power is distributed. The fact of the matter is that the bourgeois are a tiny percentage of the population. If we didn't accept the morality of the ruling class which endorses democracy as the will of the people and capitalism as the "most efficient and fairest system" that "creates value" (commodity fetishism), we would simply drag the bourgeois out of their mansions. But humans are irrational creatures.
I do nonetheless like libertarian Marxism and the Frankfurt School. But I'm personally more in favor of a Nietzschean/Foucaultian view that the real source of domination is the distribution of power, and I think anarchists have always had a better grip on this than Marx and Marxists. Anarchists have always understood that the real problem is hierarchy itself, and that even if we and Marxists share the same goal of a stateless society, you cannot actualize that if you continue to reproduce the logic of hierarchical societies. Though to be fair, classical anarchism has come rather close to being as naive as Marxism insofar as it has ignored certain hierarchies like sex and race, or ideology, formal organization, and forced collectivism. But nevertheless, anarchism's engagement with questions of the State has always put it one step ahead.
