"The veiling originally was more about the mixture of class and gender than sexuality. 'Not confined to Muslims, it [the veil] was an urban phenomenon associated mostly with the upper classes. Christian Coptic women wore long veils until the early 1900s when Western Christian missionaries influenced them against it. Most discussions are in relation to women, while men have also had a variety of head coverings, which are discussed in terms of dress codes and status' (Barbara Aswad, 'Veil: Modesty, Privacy and Resistance. Fadwa El Guindi. New York: Berg, 1999. 242 pp' [Book Review], <http://www-rcf.usc.edu/~elguindi/AARvuVeil.htm>)."
The hijab or full body dressings are prescribed in the Qur'an, the composition of which most people date to about 700 - 750 AD / CE. In it, the prescriptions for female dress are much more severe than male dress. Veiling / hijab / burqas and the like aren't the products of Western colonialism.
Yes, women in Europe have worn various types of veils, headscarves, etc., historically, but the fact remains that they certainly don't now [except anomalously], while women in Muslim countries continue to do so, just as they have since way, way before the Middle East was ever a European conquest.
Not everything in the world redounds to Western evil. In fact the URL you gave says this: "It [the veil] is tied culturally to a particular area of the world where it is related to geography, patrilineal and patriarchal social structure, class, and political movements." Patriarchy, patrilineal, gender issues = issues of sexuality.
The Qur'an prescribes the same conservative dress for women regardless of their class, and has for about 1300 years now. [The Bible does, too, but it's rarely adhered to.]
B