Persons of good will often disagree about religious beliefs. A particular problem in democratic states with government schools is that if a religion is taught, some taxpayers will support a religion against their will. This is considered unjust.
A complementary problem is that religious beliefs have historically socialized people's behavior and morality. A school that fails to teach the beliefs of the majority of the society has failed the majority of people in that society.
Many religious schools provide excellent, inexpensive education, often superior to government schools.
Religious education varies wildly around the world.
In the U.S., religious education is usually a supplementary "sunday school" taught to children while their parents attend church. Jews, Muslims, Christian Orthodox and other religions with substantial doctrines generally send their children to special classes at a place of worship after public school. Many families believe supplementary religious education is inadequate, and send their children to private religious schools. Most faiths have college and graduate-level relglious schools, but they are private. Religious education is forbidden in public schools, unless all religions are treated as equally true. There is a strong tradition of public tolerance of individual religious choices, and this is thought to be a "natural" characteristic somehow caused by the nation's constitution.
Most European countries and some of their former colonies maintain a state-supported religion. It is usually either Lutheran or Roman Catholic. It is taught in a special class of the government schools. This is a conscious policy to build and maintain a national identity. In many ocuntries families can get permission to withdraw children from these classes. Many families with other religions use religious schools. The state supports one (usually) central seminary which trains pastoral staff for the state church. Other religions may support private seminaries, but these are small and poorly funded. Religions other than the state religion, even if ancient and respectable, are usually deprecated in the national cultures (e.g. they are called "cults" in the news media).
In traditional Islamic education, children are taught to read, and sometimes speak Arabic and memorize the major suras of the Koran. Many countries have state-run schools for this purpose. Traditionally, a settlement may pay a mullah to teach children. In many Islamic cultures, education for women is thought unnecessary, although in all islamic cultures, families often work hard to afford schools for their daughters. There is a historic tradition of clever Sufi mullahs who wander and teach amusingly, and an ancient tradition of religious universities. Religious scholars are often serve as judges, especially for criminal and family law (more rarely for commercial law). Nonislamic religions are tolerated as personal beliefs, but not as public teaching. Most islamic countries have laws against teaching other religions, and especially against attempts to convert islamic believers.
In the People's Republic of China, religious education is banned, except in licensed schools of theology, which are usually college-level and above. These colleges are state-supported, and usually very small, with limited enrollments and budgets. Religious education usually occurs in scheduled sessions in private homes. Religious teachers usually move on a weekly or monthly circuit, staying as guests in private houses in exchange for teaching.
In Thailand, Burma and other homogeneously Buddhist societies, Buddhist beliefs are taught in school, often by monks. Young men are expected to become monks for several years.
In Japan, Buddhism, Confucianism, and Shinto coexist. Relgious instruction normally occurs in temples as a part-time voluntary activity, reinforced by public ceremonies and parades.