Long and complicated story – short post, but:
In Denmark, the face of an immigrant is that of a veiled woman. Immigrant men and women who do not wear veils do not exist in the political discourse.
There are several political ironies here:
The veil (Muslim or not) is intended to mark a limit between the public and private sphere and it indicates that women do not belong in the public sphere whereas men do. But would immigrant women appear as such in the political sphere in today’s Europe if they did not wear veils?
Traditionally, liberalism and conservatism assert the delimitation of a private sphere which should not be the object of political action (parallel: The debate over whether parents have the right to hit their children or not – liberals and conservatives defended the rights of violent parents with reference to privacy). Now, liberals and conservatives want to regulate† what clothing people wear in their own homes.
On the other hand, socialists and radicals traditionally questioned and rejected the delimitation of a private sphere (“the private is political”). Now, the socialists and radicals want to promote the display a sign of the public/private delimitation.
All of this of cause only applies if the object of the political discussion belong to the out-group. So to the liberals and conservatives, intruding in the private sphere is okay, as long as the objects are Muslim.
To the socialists and radicals, upholding a private sphere is okay, as long as the objects are Muslim.
PS: Yes, I am aware of the fact that there are (lots of) Muslim women who do not wear headscarves or veils.