Firstly, as far as I read this post doesn't talk about criminals hiding behind masks or veils, it's about a law which cuts freedom of religion, while this countries claim, that there is freedom of religion; this is completlely hipocracy. If this countries would state, that there existes a restriction in freedom of religion nobody could argue about a ban.
Secondly, it's ridicoules to compare a veil with being naked. But for the sake of the discussion, even if it would be a halfway good comperisson, your statement is only partly true; there are resorts and places where people can be naked, even if the laws of those countries prohibited nudity in public; whereas the same countries didn't create the same resorts for women with veil.
Thirdly, the laws which prohibits women to cover their faces didn't exist 30-40 years ago, as you mentioned; according to BBC news even in the country you are from this law is very new. A law banning the full-face veil came into effect in Belgium in July 2011 (see http://www.bbc.com/news/world-europe-13038095)
Forthly, as far as I understood, nobody talked about so-called muslim countries, where no rights for whomsoever exists anyways; the post was talking about western version of switched freedom.
Fifthly, faceveils were uncommon 30-40 years ago in Europe, but they are part of the European and Christian tradition. In Albania many christian women still wear a white veil; Coptic christians also wear veils, like the ladyin this picture.
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Even in the United States a veil is nothing uncommon. As you easily can see, even the first lady was wearing a face veil.
Sixthly, there are still many exceptions to the face covering law; e.g. women are allowed to wear a veil during wedings, during furnerals, during carneval etc. Police, special commandos, military still is allowed to wear masks, even after this law.
Seventhly, there is no logic in making a law of prohibiting the veil to prevent crime; even if there were people with veil who commited crimes, it would be a small minority. You can't make laws according to minority, sometimes, maybe happening events. So this law is not preventing crime, but it is a discrimination.