Private Muslim schools in Denmark are allowed to insist that girls wear headscarves, usually from the age of nine or ten. Public schools are not allowed to forbid Muslim girls from wearing either headscarves or hijab, but can demand that they do not cover their faces.
Some shops, the Co-op for one, allow their female workers to wear headscarves as does the railway company, others do not - it is up to the employer to stipulate workers' dress code.
Neither schools, nor places of work can forbid Jewish men and boys from wearing their skull-caps (kippah/ kippot).
Men of any denomination may be told that they may not wear shorts at work and most firms of lawyers still prefer to see their female employees in skirts and stockings rather than trousers. I believe, but am not entirely sure, that SAS still requires their air hostesses to wear bras.
Personally, I don't care for the sight of girls who are still children wearing headscarves, but the alternative would be to ban the wearing of all religious symbols in public, and I frankly would be insulted if I were told not to wear a crucifix or a medal of the Legion of Mary in public.
I agree that my understanding of the Qu'ran sura in question is that it requires men and women to dress decently, and that the wearing of headscarves, hijab, burkas, niqab etc. is a cultural matter, not a religious one, but unfortunately not all Muslims agree about this. To some it is a matter of religion.