I am not sure I agree entirely with this judgement as it pertains to burquas and headscarfs because I am not comfortable with defining a burqua as a purely "religious sign". While it is certainly associated with Islam, it is also a piece of clothing. Wearing a burqua simply means the woman is dressing conservatively/modestly in a way which makes her feel comfortable.
Maybe another way of putting this: Given the cultural background of many conservative Muslim women, they would feel the same way going out in public not wearing a headscarf as many western women would feel going out in public not wearing a shirt.
This could really set a pretty bad precedent to be honest. If a Christian woman buttons up her top all the way to the top, or wears longer dresses than her colleagues because she is more conservative than them, should the company be allowed to dictate that she wear more revealing clothing?
What about men and facial hair?