Oliver Roy has a fascinating article, The disconnect between religion and culture, in Eurosone.
There are many different ways to define secularization. As a social phenomenon, it is not an abstract process; it is always the secularization of a given religion, whose nature changes as secularization unfolds. Common definitions of secularization include three elements.
The first is the separation of state and religion, of politics and confession, without necessarily entailing a secularization of society. The United States is a good example: although there is a strong separation of church and state, levels of religiosity among the population are still high. The First Amendment of the American Constitution stresses both secularity and religious freedom. The second element in definitions of secularization is the decline in the influence of religious institutions in societies. Activities such as healthcare and education are now managed by the state or the private sector. In Europe, the churches have clearly withdrawn from the "management of society".
The third element in definitions of secularization is what Max Weber called Entzauberung – the disenchantment of the world. This does not mean that people become atheists, but that they care less about religion. Religion no longer plays a major role in our everyday lives, even if we still consider ourselves part of a religious community. In this sense, secularization corresponds to the marginalization of religion in society, rather than its exclusion.
In terms of the separation of politics and religion, all contemporary states are secular – including theocratic states. A secular theocracy might sound like a contradiction in terms, but it is important to recognize that a secular state is one that defines what religion is, not vice versa. In one of the few theocratic states in the world today, the Islamic Republic of Iran, the head or the "guide" is a politically appointed figure; no such institution ever existed in Islam. The guide is elected by means of a complex constitutional process, not because he is the highest religious authority.
Read the whole article, which is relatively short, and which concentrates on the Islamic world.
As soon as one accepts the idea that religious belonging is an act of free will, one can accept democracy, and vice versa. In my view, this debate is now taking place in Muslim countries. The new Tunisian constitution is the first constitution in an Arab country to guarantee freedom of consciousness and freedom of religion. The latter is defined as a collective right, the former as an individual right.
H/t 3QD.