The head covering is not a religious requirement for all Muslims. The more extreme versions of that religion use it. Because of this there is reason to ban it. Anyone who questions this should think twice. 

Extremist movements of all kinds exist in our world. Mostly they are toxic to the general good of society by setting up a we/they situation in which the extremists view everyone else as bad. 

In the case of Islam this translates into a war on "unbelievers".

We are therefore correct to question this practice for this reason, and one more. From what I have read the female head covering is historically more a cultural affectation than a religious symbol.

Elevation a piece of clothing that prevents people from recognizing you to the status of a religious symbol would be like letting people go into banks wearing masks.

We can be reasonably certain about the intentions of anyone who walks into a bank wearing a mask.