Interesting to read your post, and I do not doubt that the information you quote is what you actually heard on the programme you refer to, but it is not quite accurate.
Muslim women and girls may wear a head-scarf or full hijab in public if they want.
What lawgivers are seeking to stop, is small girls from the age of six being forced to go to ordinary council or private schools wearing headscarves.
As a teacher, I am not happy about this prohibition, as I would honestly rather see all immigrant children in the state schools, or in private schools that accede to the same norms, than shut away in private fundamentalistic Muslim schools, as many although not all of them, do not comply with the Government white papers on education.
What Muslim girls and women may not do, is to present themselves for oral or written exams completely covered by a burqua and face veil, and just try to prove their identity by waving their passport or national health card at the examiner.
One woman in a burqua with the lower half of her face covered or masked looks very like another, and we need to be sure that we are examining the candidate whose name in on our list, rather than her sister, cousin or class-mate who feels more certain of passing the exam.
Danish citizens, and foreigners living here may not be masked in public -this was brought in years ago following some terrorist attacks. A bus driver or train ticket controller has the right to deny a masked person entry to the vehicle.
No physician or surgeon will be willing to treat a woman who refuses to let her face be seen as proof of her identity.
The so-called ghetto question, is partly a matter of slum clearance, partly a matter of wishing a more even distrubution of members of different ethnic groups, in the various houseing schemes and partly an attempt to stop the growing number of teenagers , both children of immigrants and children of people whose ancestors have lived in Denmark since the Stone Age, from adopting the "gang culture" they have learned is "smart" from watching certain kinds of American films.
Most immigrants, irrespective of where they come from, are decent, hard-working people, who while retaining their religious affiliations and most of the customs of their country of origin do so within the confines of the law of this country, by for instance burying their dead in coffins, as it is illegal here simply to place a shrouded corpse in the grave.
Unfortunately, there are some immigrants who do not seem either to respect our democracy or wish to learn our language, or integrate themselves. Whether it is possible to completely solve these problems or not, is hard to say.
On the bright side, some years ago, we experienced neo-Nazis defacing Jewish headstones in our cemetaries on or around November 9th. Since then, Jewish sections of the cemetaries in Copenhagen are patrolled by groups of young Jewish and Muslim men as well as by our police at the start of November. The initiative to this group was taken by the religious leaders of Copenhagen's mosques and the Chief Rabbi.
In case you are wondering 9th November 1938 has gone down in history as Die Kristalnacht.