Good point, remember the big stink the Muslims raised, was it in France?, when the women were told they can no longer wear the headgear their religion demands.

(almost unfortunately) Christianity has no such rule concerning clothing outside of clothing being modest.

Relgious or not, the "descrimination" card is one that could well be played.
In Australia at least this is a big deal, we've been moving fast toward a mindless politically correct cultural desert for some years, but occasionally we can use the rules to work in our favour.