It's a mixture of both. Whereas the West would argue religion is a product of the mind and was simply "invented" in people's heads, Marxists argue that religious illusions are a reflection of man's social organisation. This is where I'd argue the difference between "Western Atheism" and Marxism become most obvious. In Marxism, Religion isn't a giant conspiracy (or a "big lie") by the ruling classes or a complete accident, but is a superstructure reflecting the economic relations of society. It is a necessary part of social development as our understanding evolves from ignorance to scientific knowledge. In this process a ruling class unconsciously and spontaneously creates an picture of the world in its own image. As a model of the historical development of religious belief, it works something like this.
In hunter-gatherer societies, man has little understanding and control of nature. religious beliefs reflect man's powerlessness over natural forces, so people end up worshipping objects (totems) or animals as deities, often based on a kind of pantheism in which reality, nature and divinity are interchangeable. Magic plays a much greater role in these early religions, though it crops up again in later ones.
In slave societies, there is a progression from animal deities to humans as human beings gain more control over nature (e.g. from Ancient Egypt with it's Dung Beatle sun god Ra to the more human-looking Zeus in Ancient Greece). Polytheism is supposedly a reflection of the decentralised nature of power structures as civilisation evolves from tribes, city states to major empires. So for the Romans, polytheism incorporated the gods of conquered peoples in to the religion to keep the local inhabitants happy even as Roman gods from the rest of the empire were introduced.
In feudalism, there is a centralised of power in to monarchies. The emergence of Christianity in the Roman Empire represents the crisis of the slave system and the consolidation of political power as it evolves closer to Feudalism. So now there is one ruler and that is reflects as one god (monotheism). Even with the "one god" monotheistic system, everything exists within a hierarchical system reflecting the hierarchical nature of feudalism with kings at the top, lords underneath and serfs/peasants at the bottom.
Then we get to capitalism and religious authority goes from the church to the individual. The Protestant Reformation is a "capitalist" theology of individuals thinking for themselves (such as reading the bible in their own language) by fighting the "feudal" theology of the catholic church representing the more rigid hierarchical systems. Galileo makes an entrance because capitalism needs scientific knowledge to develop production, whilst the catholic church wants to preserve the integrity of the biblical account by resisting scientific challenges to christian belief.
Then we finally get to "Socialism" and Marxists say that they now have a scientific understanding of nature and society and consequently can eliminate all illusions; religious, political, philosophical and scientific. So the USSR proclaims "Dialectical Materialism" as the official ideology in 1931 and then tries to eliminate any competing ideology as both an anti-scientific ideology and a counter-revolutionary one reflecting the interests of the deposed ruling classes.
This model is adequate to give a broad overview of European history of religion, but I'm still not clear on how Indian Religions (Buddhism and Hinduism) fit in. Looking at the "opium of the people" quote in full, it takes on a much broader meaning given that religion is a reflection of those social relations:
"The foundation of irreligious criticism is: Man makes religion, religion does not make man. Religion is, indeed, the self-consciousness and self-esteem of man who has either not yet won through to himself, or has already lost himself again. But man is no abstract being squatting outside the world. Man is the world of man – state, society. This state and this society produce religion, which is an inverted consciousness of the world, because they are an inverted world. Religion is the general theory of this world, its encyclopaedic compendium, its logic in popular form, its spiritual point d’honneur, its enthusiasm, its moral sanction, its solemn complement, and its universal basis of consolation and justification. It is the fantastic realization of the human essence since the human essence has not acquired any true reality. The struggle against religion is, therefore, indirectly the struggle against that world whose spiritual aroma is religion.
Religious suffering is, at one and the same time, the expression of real suffering and a protest against real suffering. Religion is the sigh of the oppressed creature, the heart of a heartless world, and the soul of soulless conditions. It is the opium of the people.
The abolition of religion as the illusory happiness of the people is the demand for their real happiness. To call on them to give up their illusions about their condition is to call on them to give up a condition that requires illusions. The criticism of religion is, therefore, in embryo, the criticism of that vale of tears of which religion is the halo."
Opium of the people - Wikipedia
