The head covering by some RCs (Latin Rite) is a practice that is identified with fundamentalism, focus on externals (language and appearance), segregation of men and women, and refusal to accept Vatican II, which in the centralised RC church is a big deal. The link to fundamentalism and differentiation of men and women is obvious when it comes to Christian denominations yet denied by many in the case of Islam.
In the eastern Orthodox church men's hair and beards are subject to regulation. In Orthodox Jewish practice hair of both men and women is regulated.
Within these faiths there are no obscure desert sects that have access to vast amounts of money aggressively peddling the strict regulation of women's dress both at formal prayer and in everyday life.
The following is from Wiki:
Current practice
Headcovering, at least during worship services, is still promoted or required in a few denominations, such as those in the Anabaptist tradition, as well as among the more traditional Catholics. Among these are Catholics who live a plain life and are known as Plain Catholics. Many Anabaptist denominations, including the Amish, Old Order Mennonite and Conservative Mennonites, conservative Church of the Brethren, the Old German Baptist Brethren,[24] the Hutterites,[25] and the Apostolic Christian Church; some Pentecostal churches, such as the Church of Our Lord Jesus Christ of the Apostolic Faith, The Pentecostal Mission, and the Christian Congregation in the United States, like Congregação Cristã no Brasil; the Laestadian Lutheran Church, the Plymouth Brethren; and the more conservative Scottish and Irish Presbyterian and Dutch Reformed churches. Believers Church, a denomination in India that traces its apostolic succession through the Anglican Communion, holds the wearing of headcoverings among women to be one of its traditions as well.[26] In those Christian denominations which have no official expectation that women cover, some individuals choose to practice headcovering according to their understanding of 1 Corinthians 11.
Eastern Christianity
Some Eastern Catholic, Eastern Orthodox and Oriental Orthodox Churches require women to cover their heads while in church; an example of this practice occurs in the Russian Orthodox Church.[27] In Albania, Christian women often wear white veils, although their eyes are visible; moreover, in that nation, in Orthodox Christian church buildings, women are separated from men by latticework partitions during the church service.[28]
In other cases, the choice may be individual, or vary within a country or jurisdiction. Among Orthodox women in Greece, the practice of wearing a head covering in church gradually declined over the course of the 20th century, and today is only practiced by very elderly women of a particular generation that is now over 80 years old. In the United States, the custom can vary depending on the denomination and congregation, and the origins of that congregation.
The male clergy of the Eastern Catholic and Orthodox Churches often have long hair and untrimmed beards if they are monastics, but married clergy often have standard haircuts. Eastern Orthodox clergy of all levels have head coverings, sometimes with veils in the case of monastics or celibates, that are donned and removed at certain points in the services. In US churches they are less commonly worn.
Bishops, archimandrites and archpriests wear mitres when wearing their liturgical vestments, which have their own rules concerning donning and doffing.
Orthodox nuns wear a head covering called an apostolnik, which is worn at all times, and is the only part of the monastic habit which distinguishes them from Orthodox monks.
Western Christianity
In Continental Europe and North America at the start of the 20th century, women in most mainstream Christian denominations wore head coverings during church services.[29] These included many Anglican,[30] Baptist,[31] Methodist,[32] Presbyterian[18][19][33] and Roman Catholic Churches.[34] At worship, in parts of the Western World, many women started to wear bonnets in lieu of headcoverings, and later, hats became predominant.[35][36] However, eventually, in North America, this practiced started to decline,[29] with some exceptions, such as among conservative Mennonites and Amish, for example.[37] In nations in regions such as the Indian subcontinent, nearly all women wear head coverings during church services.[38] Female members of Jehovah's Witnesses may only lead prayer and teaching when no baptized male is available to, and must do so wearing a head covering;[39][40] male Witnesses are to remove any headcovering (hats) when representing even a small group in public prayer.[41] Female members of the Church of Jesus Christ of Latter Day Saints, or "Mormons", are required to veil their faces during a part of the temple worship ceremonies