So I have a secret for you. EVERY society involves people relying on each other. Even in anarchist societies, people would form tribes in order to survive.
What Marx is saying in that quote is that everyone should contribute what they can. That in no way contradicts the idea that we all have human rights.
Under Capitalism, we have less freedom because power is condensed among the elitists. Whereas with Socialism, power is more evenly spread throughout society. Things like collectivization of the means of production give the workers a voice. If anything, this is more in the spirit of human rights than Capitalism is. And we'd still have personal responsibility. We'd have more power, but we'd still have to work and take care of ourselves.