Durkheim's research was based on Australian aborigines, and in particular Totemism, where each tribe worshiped their totem, which represented their society, and Durkheim drew from this that religion is just worshipping society, as this was what they were doing.
The criticisms of Durkheim are that his research on the aborigines isn't really applicable to modern societies, which he did not consider controversial or dysfunctional religions, who go against wider society’s norms and values. Another criticism is that his definition is too broad, as things such as football, are religions according to this definition.
Malwinowksi is another functionalist, who described religion as 'offering people ways in which they can manage their tensions and reduce their anxieties during times of social disruption and crisis'. He conducted his research on the Trobiland Islanders, where before fishing in the sea, religious ceremonies were conducted. Malwinowski disagreed that religion is the worship of society, but his research is similar to Durhkheim's, as it cannot be applied to western society.
Parsons was another functionalist sociologist, but he described religion as a cultural system that 'provides more general guidelines for action in the form of beliefs, values and systems of meanings'. He believed that religion helped the consensus of society by establishing principles and moral beliefs, and that it can address problems in all societies.
He used the example of the Ten Commandments, which are accepted by everyone as being 'right', but this is not true of many other cultures and societies. He also ignores problems between religions in the same society, and did not conduct any research at all.
An overall criticism of functionalism is that it neglects many instances where religion is seen as divisive and disruptive, for example Northern Ireland.
The Marxist view of religion is quite different. Karl Marx said that 'religion is the opiate of the people', as it helps create false class consciousness, oppresses the proletariat, and discourages people from changing their current situation. The main criticism of Marx is that his ideas are now extremely out of date, and he also did not take into account pluralism.
A neo-Marxist view came from Turner, who agreed with Marx that religion was linked to economic life, but it isn't always that powerful, and isn't always there to brainwash the proletariat. Turner looked at Feudalism, which is also quite out of date, but saw religion as important for lords as it supported the view that women were of low status.
Turner did not think religion was important in modern society, as wealth is not just land ownership, and is often invested in the stock market, and other such things. Also he sees secularisation taking place, and therefore not producing the false class consciousness
A completely opposite view of Functionalism and Marxism is that of Feminism, who see religion as having a base in patriarchal ideology. To see this, they say you only need to look at the bible, where most prophets and teachers, were male, in Timothy I in the bible, it says that no females should teach in the house of the Lord, and religious organisations allow gender inequalities through beliefs they develop in which women play a subsidiary role.
Both Marxist and Feminist writers argue with Durkheim's belief that religion reinforces the conscience of society, and his research is undermined by the fact it cannot be used to help understand religions role in modern society, but only in small non-literate societies